Interesting question. I say that "Different book = Different God".
According to that formulation Jews and Christians don't worship the same God.
Christians and Muslims don't worship the same God.
And Christians and Mormons don't worship the same God.
But Catholics and Presbyterians are at least working from the same book; so they worship the same God...... differently.
But what the hell do I know about it (other than having read the Old Testament, the New Testament, the Koran and the Book of Mormon)?