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.
That is Jesus, the son of Mary - the word of truth about which they are in dispute. It is not [befitting] for Allah to take a son; exalted is He! When He decrees an affair, He only says to it, "Be," and it is.
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.
And [for] their saying, "Indeed, we have killed the Messiah, Jesus, the son of Mary, the messenger of Allah ." And they did not kill him, nor did they crucify him; but [another] was made to resemble him to them. And indeed, those who differ over it are in doubt about it. They have no knowledge of it except the following of assumption. And they did not kill him, for certain.
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:
"Allah's Apostle said, "The Hour will not be established until the son of Mary (Mariam) (i.e. Isa) descends amongst you as a just ruler, he will break the cross, kill the pigs, and abolish the Jizya tax. Money will be in abundance so that nobody will accept it (as charitable gifts)."
In Islam, We believe Jesus is a Prophet, Messenger of Allah, Spirit of Allah, Word of Allah .
O people of the Scripture (Jews and Christians)! Do not exceed the limits in your religion, nor say of Allaah aught but the truth. The Messiah Eesaa (Jesus), son of Maryam (Mary), was (no more than) a Messenger of Allaah and His Word (through which He created him), (a Word) which He bestowed on Maryam (Mary) and a spirit (Rooh) created by Him. So believe in Allaah and His Messengers. Say not: "Three (trinity)!" Cease! (it is) better for you. For Allaah is (the only) God (worthy of worship), Glory be to Him (Far Exalted is He) above having a son. To Him belongs all that is in the heavens and all that is in the earth. And Allah is All-Sufficient as a Disposer of affairs. (An-Nisa 4:171)
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.
The Messiah (Jesus, son of Mary) was no more than a Messenger, many were the Messengers that passed away before him. His mother (Mary) was a Siddeeqah (she believed in the words of Allaah and his Books). They both used to eat food [as other human beings do while Allaah does not eat]. Look at how We make the signs clear to them, yet look at how they are deluded from the Truth. (5:75)
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.
Then she pointed to him (the baby, Jesus). They said: ‘How can we talk to one who is a child in the cradle?’ He (Jesus) said: ‘Verily I am a slave of God, He has given me the Scripture and made me a Prophet; And He has made me blessed wheresoever I may be, and has enjoined on me prayer, and Zakaat (charity), as long as I live. And dutiful to my mother, and did not make me arrogant, unblest. And Salaam (peace) be upon me the day I was born, and the day that I die, and the day I shall be raised alive!’” [19:29-33]
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
وَقَوۡلِهِمۡ إِنَّا قَتَلۡنَا ٱلۡمَسِيحَ عِيسَى ٱبۡنَ مَرۡيَمَ رَسُولَ ٱللَّهِ وَمَا قَتَلُوهُ وَمَا صَلَبُوهُ وَلَـٰكِن شُبِّهَ لَهُمۡۚ وَإِنَّ ٱلَّذِينَ ٱخۡتَلَفُواْ فِيهِ لَفِى شَكٍّ۬ مِّنۡهُۚ مَا لَهُم بِهِۦ مِنۡ عِلۡمٍ إِلَّا ٱتِّبَاعَ ٱلظَّنِّۚ وَمَا قَتَلُوهُ يَقِينَۢا (١٥٧) بَل رَّفَعَهُ ٱللَّهُ إِلَيۡهِۚ وَكَانَ ٱللَّهُ عَزِيزًا حَكِيمً۬ا (١٥٨)
That they said (in boast), "We killed Christ Jesus the son of Mary, the Messenger of Allah";― but they killed him not, nor crucified him, but so it was made to appear to them and those who differ therein are full of doubts, with no (certain) knowledge, but only conjecture to follow, for of a surety they killed him not.― (157)
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
إِذۡ قَالَتِ ٱلۡمَلَـٰٓٮِٕكَةُ يَـٰمَرۡيَمُ إِنَّ ٱللَّهَ يُبَشِّرُكِ بِكَلِمَةٍ۬ مِّنۡهُ ٱسۡمُهُ ٱلۡمَسِيحُ عِيسَى ٱبۡنُ مَرۡيَمَ وَجِيهً۬ا فِى ٱلدُّنۡيَا وَٱلۡأَخِرَةِ وَمِنَ ٱلۡمُقَرَّبِينَ (٤٥)
Behold! the angels said "O Mary! Allah giveth thee glad tidings of a Word from Him: his name will be Christ Jesus, the son of Mary held in honour in this world and the Hereafter and of (the company of) those nearest to Allah. (45)
Surat 3 Ayah 45
مَّا ٱلۡمَسِيحُ ٱبۡنُ مَرۡيَمَ إِلَّا رَسُولٌ۬ قَدۡ خَلَتۡ مِن قَبۡلِهِ ٱلرُّسُلُ وَأُمُّهُ ۥ صِدِّيقَةٌ۬ۖ ڪَانَا يَأۡڪُلَانِ ٱلطَّعَامَۗ ٱنظُرۡ ڪَيۡفَ نُبَيِّنُ لَهُمُ ٱلۡأَيَـٰتِ ثُمَّ ٱنظُرۡ أَنَّىٰ يُؤۡفَكُونَ (٧٥)
Christ the son of Mary was no more than an Messenger; many were the Messengers that passed away before him. His mother was a woman of truth. They had both to eat their (daily) food. See how Allah doth makes His Signs clear to them; yet see in what ways they are deluded away from the truth! (75)
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: