What is the relationship between christianity and islam?

A:

There is a historical relationship, in that Christianity developed within the Jewish milieu as an extension of Second Temple Judaism, and then some six hundred years later, Islam developed from beliefs held by Arabian Jews and Christians, with perhaps some additional pagan and Zoroastrian concepts added.

The three religions hold some basic beliefs in common, such as worship of one God, and belief in the historicity of the Old Testament accounts.
These three religions are similar beacuase they all revolve around the same books of The Bible. These books are the Hebrew Bible, which Jews follow. The Christians add the New Testament (plus or minus several books for catholics and mormons). Then the muslims add more books and the story of Mohammad. Though the biblical differences can be seen, the most arguable difference is on Christ. Jews believe that he was not the messiah and are waiting for the coming of the messiah. The Christins believe that Jesus was the messiah and are waiting for his second coming. The muslims do not believe the Jesus was the son of God, but do hold that he was a prophet. There are more differences on the requirements for salvation, but they are finicky and long. If you need more info let me know.