The debate, which I remember too, was about the fact that Jews, Christians and Muslims evolved from the same original faith- that is from the 'sons of Abraham'. Jesus and Mohammed are recognised as prophets in the teaching of Islam, but Jesus is not the Messiah. I am not sure of this, but I think that the Messiah is still to come in the Islamic faith, as he (not she in this instance I feel) is still to come in the Jewish faith.

So the God of each of these religions is, if not the same, at least closely connected.