Both Christians and Muslims worship the same God.
From the Catholic Church Catechism:
841 The Church's relationship with the Muslims. "The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind's judge on the last day."
John 4:24 "God is spirit, and those who worship Him must worship Him in spirit and truth." (Jesus Speaking)
John 14:6-7 "Jesus said to him, 'I am the way, the truth and the life; no one comes to the Father, but through me. If you had known me, you would have known My Father also.'"
John 1:18 "No man has seen God at any time; the only begotten God, who is in the bosom of the Father, He has explained Him."
(John 3:16) "God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have eternal life."
The same God?