"Whenever it is postulated that Christians and Muslims worship the same God, there are some -- both Christians and Muslims -- who say this is simply untrue. Those who raise objections generally agree that Christians and Muslims worship one God, but will not accept the statement that they worship the same God. Admittedly, this problem is probably more of a Christian problem than it is a Muslim problem. Once a Muslim is ready to acknowledge that God can be known by a name other than Allah (i.e., God. Onyame, etc.), he will generally agree that Christians and Muslims worship "the same God." At the same time, he will insist, however, that Christians err in "associating" (shirk) others with God. This conclusion grows out of the common misunderstanding among Muslims, based partially on the Quran (5:119), that Christians worship a Trinity of Father, Mother, and Son.
The problem as it confronts Christians is another kind of a problem altogether. It is a question of whether you can say you are worshipping the same God when you have such different understandings of the nature of God. Those who are troubled by this concern say that although Christians and Muslims use the same name for God and many of the same words to describe Him, they are not talking about the same God because Christians are talking about the Triune God, Father, Son and Holy Spirit..." --excerpted from "REACHING MUSLIMS FOR CHRIST: A Handbook for Christian Outreach Among Muslims" by William J. Saal (Chicago: Moody Press, 1991) (© 1991 Arab World Ministries).