Do We Worship the Same God as Islam?

There's a sense in which someone can refer to a thing under a false description.  Take it that I try to refer to a woman in the corner by the following description: "The woman over there drinking coffee," while the woman is actually drinking water.  We'd take it, I assume, that I've successfully referred to the woman despite my including a false description.  

So I think it's possible that Islam oftentimes successfully refers to God under false descriptions, e.g., "God inspired the prophet Muhammad," while being a false description, seems to attempt to pick out what we usually mean by God.

Still, despite being able to successfully refer to God under false descriptions, it doesn't follow that Islam's conception of God is acceptable.  I think that it isn't.  Their conception of him fails to understand his gracious and loving nature.  So, in one sense, while they successfully refer to him, they refer to him with idolatrous and wrong descriptions, substituting a false image of him for the truth of his character.  God wants us to have a right conception of him, and relate to him as he truly is.