This is a hotly debated question, and the way you have formulated it highlights the greatest bone of contention. Christians and Muslims with an ecumenical approach stress the similarities between Yahweh in the Bible and Allah in the Qur'an, translating both as "God" and affirming that Jews, Christians, and Muslims all worship the same omniscient, omnipotent deity, the Creator of Heaven and earth.
However, Christians believe that Jesus Christ was the son of God. Muslims accept many of the Christian assertions about Jesus, and he is the most frequently mentioned figure in the Qur'an. However, Islam specifically denies that Christ is the son of God or that God has any son at all. For instance, verse 17.111 of the Qur'an reads,
Praise be to Allah, Who hath not taken unto Himself a son, and Who hath no partner in the Sovereignty. (Pickthall translation)
There are many other points of contention, but this is the essential one. It is the central claim of Christianity that Christ is the son of God, and Islam flatly denies this is possible.
One possible solution, however, lies in the two names used for "God" in the Old Testament. Some theologians have argued that Yahweh and Elohim, the two names used by two different scribes, are actually different gods, or different aspects of God. Yahweh is identified with the tribal god of the Israelites, while Elohim is the Creator God. If one accepts this hypothesis (which is seldom discussed by Christians except in academic theology), then it would be possible to identify Allah with Elohim and say that Christ was the son of Yahweh. This gives rise to various complex questions for Biblical and Qur'anic scholars, but it does provide a clear reason for the difference between the Father of Jesus and the Allah of Muhammad.