Islam is literally a form of Satanism.
So I don’t see how there could be any question of the two faiths worshiping the same God.
If you want to understand Islam, read “Paradise Lost”.
No other book so clearly elucidates Satan’s hatred for God and the extents to which he will go to gain revenge on God for casting him out of heaven.
Islam is easy to understand if you can grasp one concpe: It wasn’t the angel Gabriel who appeared to Mohammed; it was Satan disguised as Gabriel. Once you accept that, everything about Islam makes sense.