Both religions acknowledge the existence of Jesus of Nazareth. But how do the Muslim teachings about Jesus differ from the Christian view of the same person?
Here are the points where Islam differs with (mainstream) Christianity when it comes to the person of Jesus:
1. Islam does not recognize Jesus as the son of God
In Islam, Jesus is a messenger of Allah and among the five greatest known as Ulu Al-Azm (those of great resolve). And while he is a great and righteous man gifted with many miracles, he is not divine in any way.
2. Islam does not teach that Jesus was crucified and reserructed
Muslims believe that Jesus did not die on the cross, but was in fact ascended up to the heavens where he continues to be alive. The majority view is that Jesus was ascended just before the crucifixion event and was replaced by someone else. It only appeared that Jesus was crucified, when in fact someone else had replaced him. There is no clear evidence on the identity of the person who replaced him, but many believe that it was Judas Iscariot.
3. The second coming of Jesus
Muslims believe that in the end of days, Jesus will descend again to help the Mahdi and the Muslims in their war against Al-Masih Ad-Dajjal (the charlatan messiah). Details differ among scholars and schools of thought. See this Hadith:
In Islam, We believe Jesus is a Prophet, Messenger of Allah, Spirit of Allah, Word of Allah .
This verse was revealed in relation to various factions of the Christians (Ya'qubiyyah, Nestoriyyah, Malikaaniyyah, Marqoosiyyah), and they had various sayings so some said, "Jesus is Allaah", others said, "He is the son of Allaah" and others said, "He is the third of three." Source: Jesus in Islam
And he is the blessed Messiah and no more than a Messenger. He was humble servant and worshipper of Allah.
Moreover, Christians believe Jesus is dead. But, we believe that Jesus is alive and he will return upon earth at the appointed time near the approach of the Hour when he will kill al-Dajjaal (the great liar), and he will abide by and establish Islaam, and there will be none from the people of the book (Jews, Christians) except that they will affirm their faith in him and his essential message of Islam.
More subtle differences in belief:
Both Christians and Muslims believe that Jesus could perform miracles. But, Christians believe it was his own power but Muslims believe it was through the power given by Allah.
Christians believe that Jesus was crucified
Muslims do not, We believe that He ascended
Surat 4 Ayah 157
Christians believe that He is the son of Allah, and sometimes Allah Himself, Auzubillah.
Muslims believe that He is a Prophet of Allah
Surat 3 Ayah 45
Surat 5 Ayah 75
In the Qur'an, in a passage describing the annunciation to the Blessed Virgin Mary, Jesus ('a) is described as a Word from God: "O Mary! Verily Allah gives you the glad tidings of a Word from Him; his name is the Messiah, Jesus son of Mary, eminent in this world, and in the Hereafter of those near [to God]" (3:44)
The context in which this ayah was revealed was one of inter-religious encounter. It is said that the Christians of Najran sent a delegation to the Prophet of Islam (s) at Makkah to question him about the teachings of Islam concerning Jesus ('a), and God revealed the above and other ayat of Surat Al 'Imran in response. The response is not only not a denial of Christian teachings, although the divinity of Christ is clearly rejected, but also an affirmation of much believed by Christians as well, even the designation of Christ as logos: 'O People of the Book! Do not go to extremes in your creed, and do not say of Allah but the Truth. Verily, the Messiah, Jesus the son of Mary, is only an apostle of Allah and His Word which He conveyed unto Mary, and a Spirit from Him (Qur'an 4:171) So in addition to being called the Word of God, Jesus ('a) is also called a Spirit of God and in some of the narrations reported in the Shi'i tradition, this title is used.
Please look at these two: