OK! HERE I GO!!!!! AHHHH I'M SO EXCITED!
The words are meant to refer to the same entity.
Elohim is a plural intensive form, meaning the 'im' at the end indicates the greatness or multitude of powers related to the main part which is most often transliterated as Eloah but what is being transliterated is actually A.L.H Alif being the first part which is a glottal stop, pronounced like "uh" so the word is pronounced Uhllaw in semitic languages (which includes Akkadian, Hebrew, Aramaic, Amharic, and Arabic mainly).
Ellaha or Allaha or Ellah are all roman text transliterations of the word meaning God, always pronounced Uhllaw.
All these words refer to God. Some say that Allah is a combination of Al and Ilah meaning The God, and it also has an extra L in it but these aren't really serious points because it is just the Arabic word meaning God or The God, the Supreme God, while Illah means something that is worshiped or a power or something, and the Muslim creed is generally There is no Illah but Allah which can be translated as there is no deity (or anything worthy of worship) but The (Ultimate) God.
Anyway, despite being the same word, with the same root, and the same meaning THEY ARE DIFFERENT!!!!!!!!
THAT IS THE PART I WAS EXCITED ABOUT! AHHHHHHH!
Why are they different? Well! Muslims generally consider the Qur'an as the primary source text which deals with most matters pertaining to their religion.
The Jewish people consider the books of what is called the Old Testament or the Hebrew Bible or Torah to be a primary source text for their religion.
The Christian people consider the books included in the Bible considered most relevant to their sects to be the most important source text for their religion, and this often if not always includes the Hebrew Bible, also called the Tanakh.
The Muslims often say that Allah and the God of the Bible are the same, and the Qur'an itself affirms that the God of the Christians and the Jews is Allah, and the same word is used by them all (this is especially uncontroversial among Arab Christians and Arabic speaking Jews)
Though the Muslims often say this, it is likely that most muslims are unfamiliar with what the Bible actually contains when they say this, and assume it is similar to the Qur'an and contains the Qur'an's stories.
Though the stories in the two books have similarities at times, and the names of the people mentioned seem to be references to the same characters among the two books in many cases, the books are very different and the way the characters are described and the stories that are mentioned about them and the attitude with which they are dealt is entirely different.
If a sincere Muslim who knows the Qur'an well and has a sincere admiration and love for the characters mentioned in the Qur'an were to read the Bible carefully, though would likely reject it outright, and may become extremely angry about what is contained within.
This is because the Qur'an describes the characters mentioned in the Bible in a very positive light, they appear to be really good, sensitive, kind hearted people, while the Bible describes them in ways that the sincere Muslim would find almost totally abhorrent.
Similarly, the way the Bible describes God is different in some ways from the way the Qur'an describes God, and the way the God of the Qur'an talks is different from the way the God of the Bible apparently seems to talk.
The way the God of the Bible seems to be described would also likely insult Muslims who are well versed in the Qur'an.
The Qur'an explains this similarly to how Jeremiah 8:8 explains it, the scribes apparently altered the Torah during its years of transmission, and it ended up corrupted from the original form it was given in, which the Muslims might believe would resemble the Qur'an more.
The Qur'an is different from the Bible because of the style it is written in. It is written as though God is speaking directly to the reader (or Muhammed).
The God of the Bible commands things that the God of the Qur'an would appear to be against, for example the command to massacre all the women, children, and suckling babies, as well as all the animals of the Amalekites.
To put it simply, though the God of the Qur'an does promise punishment for evil people, the God of the Bible is different in several ways due to the way the God of the Bible seems to over-do it sometimes and also has regrets and things that the God of the Qur'an doesn't have.
One could say the God of the Bible is more human seeming, while the God of the Qur'an is clearly not intended to be a human or anything with a form, but rather the Ultimate Reality and Power which sustains all life and experience, animating it, and ultimately controlling it precisely, pervading everywhere, inside and out, closer than the jugular vein, surrounding everything everywhere.
The Bible has verses which confirm this idea of God, but also has verses which seem to depict God in more anthropomorphic terms more often than the Qur'an.
The Jewish idea of God is similar to the Muslim idea on the surface, but since they rely on different books for the idea, and the God performed various acts differently, the God ends up being different in some ways. The Muslim will hopefully not find a need to justify the atrocities demanded by the God of the Bible, since they could easily reject such things as a corruption, since the God of the Qur'an does not behave like that generally.
The Jews and the Muslims both generally believe in an Ultimate God when they are well versed in the scriptures, and this goes for the Christians as well, BUT:
Many Christians, and perhaps some less knowledgeable Jews may imagine God as a humanoid form, an old man in the sky, with immense power, but with the passions of a person in many senses.
Most Christians (Catholics being the largest sect currently, followed by other Trinitarian sects such as the majority of Protestants) came to believe in a Trinitarian God after the various councils held and enforced by Roman authority.
The Trinitarian God is very different from the God of the Muslims, and also different from the God of the Jews despite Christians depending on a large number of texts that the Jewish people also use.
The Oneness of Allah or the Monotheism in Islam is an important factor in Islam, and this is called Tawheed.
The Trinity appears problematic to Muslims, who might consider it an act of 'shirk' which means the "sharing" of power with Allah, basically to say there are other powers, forces, or identities besides Allah which are co-creators with Allah.
In Mormonism, Elohim is considered God the Father, while Jehovah (a European transliteration of YHWH) is considered Jesus. Together with the Holy Spirit, they make up what is called the "Godhead" while being three distinct entities, like a team, and at least God the Father and Jesus both have bodies, and Jesus is the literal son of God while the Holy Spirit remains bodiless.
Mainstream Christians are generally supposed to believe that God, Jesus, and the Holy Spirit are actually all different aspects or manifestations of the same One God, and thus they maintain that they are monotheists, while the Mormons might be considered henotheists at best (since they often say they only worship God the Father) though many consider them polytheists.
Jesus is considered the Word (Logos) of God, co-eternal with God as God, and manifested as Jesus, the living incarnation of God and also the begotten son of God born to the virgin Mary.
The Qur'an says that Jesus is a messenger of God, and is greatly respected, and even the miraculous birth of Jesus to the virgin Mary is included in the Qur'an as a miracle of God, but Jesus is not considered the literal begotten son of God, and God is not considered a humanoid, and God has no children nor is God one to have children (since God is not considered a creature or organism or one that biologically reproduces or reproduces at all, but rather creates and manifests things from nothing, a unique ability exclusive to Allah).
The word God is used by many people, but each person may have a unique idea about what they are saying.
Though Alah and Alaheim can be alternate transliterations for the same word used in the Bible and most often transliterated as Eloah and El and Elohim, the term means to refer to the same entity, the Supreme God, though the Bible and the Qur'an are different, and the descriptions of things said and done by God between these two books may also differ.
The word was used by the Akkadians and other ancient civilizations, and Uhllah may be one of the oldest known words for God.
Here is a Jewish person explaining some of the same as I did:
Here something from the start of Clarke's Commentary on the Bible:
"As the word Elohim is the term by which the Divine Being is most generally expressed in the Old Testament, it may be necessary to consider it here more at large. It is a maxim that admits of no controversy,
that every noun in the Hebrew language is derived from a verb, which is usually termed the radix or root, from which, not only the noun, but all the different flections of the verb, spring.
This radix is the third person singular of the preterite or past tense. The ideal meaning of this root expresses some essential property of the thing which it designates, or of which it is an appellative.
The root in Hebrew, and in its sister language, the Arabic, generally consists of three letters, and every word must be traced to its root in order to ascertain its genuine meaning, for there alone is this meaning to be found.
In Hebrew and Arabic this is essentially necessary, and no man can safely criticise on any word in either of these languages who does not carefully attend to this point.
I mention the Arabic with the Hebrew for two reasons.
1. Because the two languages evidently spring from the same source, and have very nearly the same mode of construction.
2. Because the deficient roots in the Hebrew Bible are to be sought for in the Arabic language.
The reason of this must be obvious, when it is considered that the whole of the Hebrew language is lost except what is in the Bible, and even a part of this book is written in Chaldee.
Now, as the English Bible does not contain the whole of the English language, so the Hebrew Bible does not contain the whole of the Hebrew.
If a man meet with an English word which he cannot find in an ample concordance or dictionary to the Bible, he must of course seek for that word in a general English dictionary. In like manner, if a particular form of a Hebrew word occur that cannot be traced to a root in the Hebrew Bible, because the word does not occur in the third person singular of the past tense in the Bible, it is expedient, it is perfectly lawful, and often indispensably necessary, to seek the deficient root in the Arabic. For as the
Arabic is still a living language, and perhaps the most copious in the universe, it may well be expected to furnish those terms which are deficient in the Hebrew Bible.
And the reasonableness of this is founded on another maxim, viz., that either the Arabic was derived from the Hebrew, or the Hebrew from the Arabic. I shall not enter into this controversy;
there are great names on both sides, and the decision of the question in either way will have the same effect on my argument. For if the Arabic were derived from the Hebrew, it must have been when the Hebrew was a living and complete language, because such is the Arabic now; and therefore all its essential roots we may reasonably expect to find there: but if, as Sir William Jones supposed, the Hebrew were derived from the Arabic, the same expectation is justified, the deficient roots in Hebrew may be sought for in the mother tongue.
If, for example, we meet with a term in our ancient English language the meaning of which we find difficult to ascertain, common sense teaches us that we should seek for it in the Anglo-Saxon, from which our language springs; and, if necessary, go up to the Teutonic, from which the Anglo-Saxon was derived.
No person disputes the legitimacy of this measure, and we find it in constant practice. I make these observations at the very threshold of my work, because the necessity of acting on this principle (seeking deficient Hebrew roots in the Arabic) may often occur, and I wish to speak once for all on the subject.
The first sentence in the Scripture shows the propriety of having recourse to this principle. We have seen that the word אלהים Elohim is plural; we have traced our term God to its source, and have seen its signification; and also a general definition of the thing or being included under this term, has been tremblingly attempted.
We should now trace the original to its root, but this root does not appear in the Hebrew Bible. Were the Hebrew a complete language, a pious reason might be given for this omission, viz., "As God is without beginning and without cause, as his being is infinite and underived, the Hebrew language consults strict propriety in giving no root whence his name can be deduced."
Mr. Parkhurst, to whose pious and learned labors in Hebrew literature most Biblical students are indebted, thinks he has found the root in אלה alah, he swore, bound himself by oath; Most pious minds will revolt from such a definition, and will be glad with me
to find both the noun and the root preserved in Arabic. Allah is the common name for God in the Arabic tongue, and often the emphatic is used. Now both these words are derived from the root alaha,
he worshipped, adored, was struck with astonishment, fear, or terror; and hence, he adored with sacred horror and veneration, cum sacro horrore ac veneratione coluit, adoravit - Wilmet.
Hence ilahon, fear, veneration, and also the object of religious fear, the Deity, the supreme God, the tremendous Being.
This is not a new idea; God was considered in the same light among the ancient Hebrews; and hence Jacob swears by the fear of his father Isaac, Genesis 31:53. To complete the definition, Golius renders alaha, juvit, liberavit, et tutatus fuit, "he succoured, liberated, kept in safety, or defended."
Thus from the ideal meaning of this most expressive root, we acquire the most correct notion of the Divine nature; for we learn that God is the sole object of adoration; that the perfections of his nature are such as must astonish all those who piously contemplate them, and fill with horror all who would dare to give his glory to another, or break his commandments; that consequently he should be worshipped with reverence and religious fear; and that every sincere worshipper may expect from him help in all his weaknesses, trials, difficulties, temptations, etc.,; freedom from the power, guilt, nature, and consequences of sin; and to be supported, defended, and saved to the uttermost, and to the end."
YHWH is a term used in the Bible, which appears to mean the following:
"he word YHWH is made up of Y, meaning "he", plus a form of HWY, the root of a group of words connected with "being" and "becoming". Frank Moore Cross has advanced the hypothesis that the name Yahweh is an abbreviation, in which the theophoric element el has been dropped, thus giving yhwh-'l or "El-Yahweh", which would parallel "El-Shaddai" and "El-Elyon". El was the chief god of the Canaanite pantheon, and El-YHWH is still attested as an epithet, 'El, who shows himself' in a few places in the Old Testament (in Psalm 50:1, for example). It would have originated as a description of El's appearance and blessing: "El who shows himself"."
^ 'It is generally accepted that this name is a yaqtil-form of the Semitic stem HWY ('to be').'Stefan Paas, Creation and judgement: creation texts in some eighth century prophets,BRILL, 2003 p.137
^ However, nowhere in the Old Testament has any trace been left behind on the complete name yhwh-'l.' Stefan Paas, ibid. p.138.
^ Paas (2003), pp.137–139