Whether one prefers to say that Muslims, Jews and Christians believe in different gods, as opposed to differing views of the same god, is largely a matter of semantics. From a Christian perspective, anyone who does not accept the full revelation of God through the saving work of Christ and the sustaining presence of the Holy Spirit has only a partial understanding of God.Thus, Christians might argue that Muslims or Jews worship "a different god" because we believe their concept of God is incomplete. It is perhaps more appropriate, however, to think of Muslims and Jews as worshiping the same god, though not in His fullness.
Why does it matter? Our terminology can impact the effectiveness of our witness to any who do not accept Christ. It is essential that we keep channels of communication open by showing respect for people of other faiths, even if we believe their view of God is inadequate. Explaining Christ as the saving fulfillment and ultimate revelation of the same god is a natural and effective means of sharing our faith with Muslims and Jews. Insisting that they worship a different god altogether is bound to be counter-productive.
It is possible to be tactful in our speech without compromising our witness. --Source