Many claim the Muslims worship a different, "pagan" God, not the same as Christianity or Judaism. This is false. The God of Islam is the same Yahweh, the God of Abraham, Issac, and Jacob. If we study history, culture, language and etomology, we can easily see this.
In Meccs in Muhammad's time, there were many shrines to many Gods. Like most polytheists, the Arabs wanted to hedge their bets. So they built Shrines to any Deity they came across, so as not to offend one.
Muhammed had a dream: the Angel Gabriel came to him and commanded him to write the Koran, as God's final revelation. So Muhammad began to preach Allah as the One True God, and all others were false Gods. Naturally he was prosecuted for this.
Allah can easily be proven to be Yah (weh); the God of the Jews & Christians. If you look at the etomology of the Name:
Al(The)-Il/El(God-Iah (Yah): The God Yah!
The difference between the religions, is NOT whether it's the same Deity; rather what they believe about that Deity.
Of course Jews do not have a Trinitarian God; but that doesn't make it a "different god"; only difference is belief and practice.
Does the Islamic Faith differ from the Christian? Of course! So does the Jewish Faith. Difference in theology doesn't make for a different Deity.