This is an interesting question. Years ago, I copy edited the book Handbook of Denominations in the United States. Its editor refers to Judaism, Christianity, and Islam as Abrahamic religions, meaning that each one claims the Old Testament figure Abraham as being central to their faith.
Other similarities between Christians and Muslims:
- monotheistic; i.e., belief in one God, whom Muslims call Allah
- belief in an afterlife and a final judgment
- belief in the existence of angels
- prohibition of idols
Some of the differences:
- Christians: Jesus is the son of God and savior of humanity; Muslims: Jesus was a prophet and Mohammed's teachings lead to salvation
- Christians: no dietary restrictions (except in some denominations); Muslims: no pork or alcohol may be consumed
- Christians: The Bible, consisting of the Old and New Testaments is the sacred book; Muslims: the Qu'ran is the sacred book
- Christians: Jerusalem is the holy city; Muslims: Mecca is the holy city
- Christians: men and women worship together; Muslims: men and women worship separately in the same building
- Christians: allowed to debate literal meaning of the Bible texts; Muslims: religious texts are infallible
- Christians: relate religion to daily life incorporating secular culture if possible, e.g., music; Muslim: rejection of secular life and insistence on return to "pure" Islam
These are only a few of the similarities and differences between the two religions. Visit the links below for more info.