Do Muslims and Christians believe in the same God? No. The main difference is Jesus. Jesus is God, and is called the Son of God. Jesus is mentioned in the Koran, but only as a prophet, not as God. In the Bible, Jesus is God (John 1:1, 14; John 5:18; John 8:58; John 20:28; Colossians 2:9; Hebrews 1:8). 

Another difference is that the God of the Bible is Love (1 John 4:8, 16) and His followers are known by their love. Very different from the Koran and its followers. Here is an article that examines the use of the word “love” in the Koran and its absence as a character quality, unlike the God of the Bible: “A Study of the Word Love in the Qur’an.”

Finally, here is a clip from an excellent article written by a former Muslim for the Ravi Zacharias International Ministries website. The article is titled “Do Muslims and Christians Worship the Same God?“:

“Let’s start with the obvious: Christians believe Jesus is God, but the Quran is so opposed to this belief that it condemns Jesus worshipers to Hell (5.72). For Christians, Jesus is certainly God, and for Muslims Jesus is certainly not God. How can it be said that Christians and Muslims worship the same God? This fact alone is enough to settle the matter, but at the very least, no one should argue as Volf has that “there isn’t any theological justification” for believing Christians and Muslims worship different Gods. There certainly is, and it is the obvious position when we consider the person of Jesus.

Another difference between the Islamic God and the Christian God that is quite personal to me is his Fatherhood. According to Jesus, God is our Father, yet the Quran very specifically denies that Allah is a father (112.1-4). In fact, in 5.18, the Quran tells Muslims to rebuke Jews and Christians for calling God their loving Father because humans are just things that God has created.

The same is the case when we consider the doctrine of the Trinity. Islam roundly condemns worship of the Trinity (5.73), establishing in contrast its own core principle: Tawhid, the absolute oneness of God. Tawhidspecifically denies the Trinity, so much so that it is safe to say the doctrine of God in Christianity is antithetical to the doctrine of God in Islam. Not just different but completely opposed to one another.

There is much more to be said about the differences between the Christian God and the Muslim God, but this much can already be said with confidence: the Christian God, both in terms of what he is (Triune) and who he is (Father, Son, and Spirit) is not just different from the Muslim God; He is fundamentally incompatible. According to Islam, worshiping the Christian God is not just wrong; it sends you to Hell. They are not the same God.”

You can read the full article here: http://rzim.org/global-blog/do-muslims-and-christians-worship-the-same-god 

Also, at the GotQuestions website you’ll find the article “What Does it Mean that Jesus is the Son of God?”