Muslims are pretty clear that they worship the one true God of the Bible (they share the OT with Christians and Jews and are well aware of who Abraham's God was/is) and not the moon. Too bad you're confused.
Actually, Muslims accept (to a degree) only the first 5 books of the Old Testament, not the whole OT. And, regardless of their clarity, the identity of their god is only one of many things about which Muslims are confused.