I never stated that they were the same word. They have the same root, since both Hebrew and Arabic are descended from the common ancestral Semitic language. In the romance languages, there are very similar words in Spanish and French that are both descended from Latin.
The Hebrew Bible uses the terms el and elohim (among others) to refer to Almighty God. Not sure about elohim, but the word el is also freely used to refer to pagan deities, just as we use the common noun "god" today. In pre-Islamic times, allah was used similarly. With the rise of Islam, the term Allah became limited to the God of Abraham, just as the capitalized term God was for Christians.
Interestingly enough, far and away the most common term for "God" in the OT is YHWH, transliterated into English as Yahweh or Jehovah. This is a name or proper noun never used to refer to any other god, unlike the common noun el or god.
since for obscure reasons most modern Christians have dropped using this name, we're stuck with the confusion created by using a common noun as a Name.
You might be intersted in this link. http://en.wikipedia.org/wiki/Allah
I am fully aquainted with the theology, evolution and etymology of the words in the original OT texts...
not the same.