Difference between El and Eloah

Question

El(אל) and Eloah(אלוה) are both singular forms (nouns), but its אל thats being used to form the plural Elim (אלים), and אלוה thats being used to form the plural Elohim (אלוה׳ם). Both singular forms seem to be closely related to eachother. But what exactly is the connection and the difference (in grammar and, more important, in meaning) between the two? And what is the best way to define both words El(אל) and Eloah(אלוה)?

It seems that El has it's own development; El-singular, Eili-plural and Elim-collective plural.
Like Eloah; Eloah-singular, Eloahi-plural and Elohim-collective plural.

I found this online but it didn't gave answer to my question, but it gave me some insight in te grammar of both words:

El and Eloah are different, though Eloah comes from El. El has it’s own development; El-singular, Eili-plural and Elim-collective plural. It is also use for G-d and pagan deity (one individual) or deities (many individuals, separated or collective). El simply means strenght (as in mighty one). Elohim or Eloahim is derived from Eloah, the plural of Eloah is Eloahi. However, both Eloahi and Elohim are the plurals of Eloah, but Eloahi is simple plural (Jurors) while Elohim is a collective plural noun (Jury). Most dictionaries states that a collective plural noun is a ‘singular noun denoting a group of individuals’. Apparently, Elohim (Eloahim) and Elohi (Eloahi) is used interchangeably. That is, where Elohim is said to be in DUE 6:4 it can also read Eloahi or some say it reads that. Eloahi is also often translated Elohe. Nevertheless, as stated, the plural form can be used for a singular subject, that is, one person, to denote majesty; as is the case with using Elohim for G-d.

Answer 1

When I was doing research for my newly-released book God versus Gods: Judaism in the Age of Idolatry (Mosaica Press, 2018), I looked into this question and found some important sources. @Zeev wrote in a comment to the question to look at the Abarbanel. What he writes is long and complicated (exactly how the Abarbanel usually writes), but here's my attempt at summarizing what he says:

Hashem has two main names: One is the Tetragrammaton which is His “personal” name and refers to His infinite being, which cannot be described nor comprehended. The other name is El, which denotes His power and influence over creation. Because the latter name does not describe Him “personally”, the Bible usually complements the name El with elements of His “personal” name. This combination can result in three types of compound names/descriptions of Hashem: When the first two letters of the Tetragrammaton are added to El, the resulting word is Elohei (א-להי), which is the construct form of the word god (i.e., “god of…”). When the last two letters of the Tetragrammaton are added to El, the resultant is Eloah (א-לוה), which literally means “god”. The third word, Elohim, is essentially the first compound with a mem (מ) appended in order to differentiate the definitive form from the construct form, so that א-להים means “god” as opposed to “god of…”. Based on all of this, Abarbanel explains that Elohim was not borrowed from another context in order to serve as another word for God. Rather, Elohim primarily refers to God, and was borrowed from that context to also refer to angels who also influence the world (in a God-like way, albeit with limitations).

Regarding why the word Elohim seems to be in plural form, I found a bunch of sources on this, and it is actually related to the Abarbanel I mentioned above:

• Ibn Ezra and R. Bachaya (to Gen. 1:1) write that the word Elohim is in plural form because it is an expression of honor to refer to an individual as if he were many. Abarbanel (to Gen. 1:1) questions this explanation by noting that the Bible also uses the word Elohim to mean idols; if Ibn Ezra is correct, then why are idols also referred to in plural if they are not due the same honor afforded to Hashem.

• R. Yehudah ha-Levi writes (Kuzari 4:1) that the word Elohim is in plural form because it is borrowed from the “gods” of the idolaters who generally worshipped a set of gods.

• Nachmanides (to Gen. 1:1) writes that the word Elohim is a portmanteau of the two words el (אל, power) and heim (הם, they are). He explains that according to this, the name Elohim refers to God’s role as the source of all powers and abilities. Abarbanel (to Gen. 1:1) cites this explanation in order to explain why the word Elohim seems to be in plural form. Accordingly, he understood that Nachmanides means to explain that Elohim is in plural because God is the holder of all powers. However, Abarbanel notes that this explanation fails to account for the extra letter yud (י) found in the name Elohim.

• R. Bachaya (to Gen. 1:1) addresses the extra yud by attaching to it some mysterious Kabbalistic implications, which he refuses to explain. R. Menachem Tziyyoni (as cited by Sefer Naphtali to R. Bachaya there) explains that the letter yud—which holds the numerical value of of ten—alludes to the Ten Sefiroth significant in Kabbalistic writings; see also R. Moshe Isserles’ Toras ha-Olah (3:4).
• In line with his abovementioned explanation, Abarbanel contends that the seemingly plural ending of the word Elohim is merely incidental, the mem at the end of the word simply serves to draw a difference between the construct form of the word god and the definitive form of the word. See also R. Meir Al-Dabi’s Shvilei Emunah (Nesiv #1) and R. Moshe of Trani’s Beis Elohim (Shaar ha-Yesodos, chs. 4–6).

Answer 2

El means power. It is used as a descriptiona as well as a name for G-d, humans, angels and even pagan gods. The plural of el is elim (powers or gods), and not “elohim." Hebrew has a full conjugation (with different forms for 1st, 2nd and 3rd person, singular and plural, masculine and feminine).

A noun by itself isn't plural (so an "im" ending doesn't always mean the word is plural -- it may just denote power). It is the verb which indicates the word’s plurality. In Hebrew a single word does not make a sentence singular or plural, and often the use of ים is found in words that are obviously singular. Elohim ends with the masculine plural suffix "ים”.

All of that is to state that the word "elohim" isn't automatically plural. The singular of Elohim is: Elo'ah, which can used to stress the Oneness even more then the seemingly plural elohim, without the limitations and “many-ness” (of each individual power) which could be inferred by: el.

The Sforno says that eloha focuses on the eternal nature of G-d, “eternity”, and el stresses decisiveness, capability, and active will.

Maimonides (the Rambam usually) prefers "elo'ah" as opposed to elohim. The T'nach, on the other hand, believes in the total Unity of elohim with such monotheistic clarity when used to speak of HaShem, that it usually uses elohim more than elo'ah, to davka stress the Unity without suspecting any kind of confusion or plurality.