The question of whether the God of Islam is the same as the God of Christianity has become a popular trending topic at the moment thanks to a controversy that has developed over a professor at a Christian university who was suspended after stating that Muslims and Christians both worship the same God.
There are indeed certain similarities between the God of Islam and the God of Christianity. Both affirm that God created and sustains the universe. Both affirm a need to worship and obey God.
However, Christians worship a God who is expressed as a Trinity: Father, Son and Holy Spirit. Christians worship Jesus as God. Islam explicitly rejects the concept of the Trinity and explicitly rejects that Jesus is God:
People of the Book, do not transgress the bounds of your religion. Speak nothing but the truth about God. The Messiah, Jesus the son of Mary, was no more than God’s apostle and His Word which He cast to Mary: a spirit from Him. So believe in God and His apostles and do not say: ‘Three.’ Forbear, and it shall be better for you. God is but one God. God forbid that He should have a son! His is all that the heavens and the earth contain. God is the all-sufficient protector. The Messiah does not disdain to be a servant of God, nor do the angels who are nearest to Him. Those who through arrogance disdain His service shall all be brought before Him.
(quotations of the Quran are from The Koran, translated by N.J. Dawood. Penguin Books, 1956, 1990)
Since the whole "Jesus is God" and "God is a Trinity" are central to Christian belief, it seems rather obvious that no, the God of Islam and the God of Christianity are not conceptually the same.
What puzzles me is that anyone would be surprised by this. Islam and Christianity are obviously not the same religion. That we both happen to be monotheistic is not sufficient to make us the same. Anyone who wants to argue that “all religions are alike” is making a statement about as rigorous as saying that “all mammals are alike.” Yeah, all mammals are warm blooded and suckle their young, but there are some significant differences between a kangaroo and an elephant.