Maybe I wasn't clear enough but what I meant was that Muslims believe that we Jews and Christians are worshipping God (their god) but we completely mis-understand who He is and what we are in relationship to Him. But it is certain that all three religions agree that there is only one true God and we are all praying to Him.

Compare this to other god based religions like Hinduism. I'm sure Muslims, as well as Jews and Christians, would say that the Hindu gods do not exist. Period.