Christianity and Islam are old cousins in Biblical terms. This goes back to Abraham and his illegitimate son Ishmael who was the son of his servant Hagar. Abraham did not believe that God would give him a son as promised and Sarah sent Hagar into Abraham to sleep with him.
Later on God did give Sarah and Abraham a son named Isaac. This son was the son God asked Abraham to sacrifice on the alter. Ishmael was the first born son but was never recognized by Sarah as such and Sarah eventually banished Hagar and Ishmael. This of course is a quick summarization of the story.
Isaac was the line that eventually lead to the birth of Jesus Christ. Ishmael was the line of which the prophet Mohamed eventually came from. Both religions believe in God or Jehovah; however, Islam does not see Jesus as the son of God.
This is maybe why people who are uniformed get confused about the two religions.