Correct...Islam does not believe in the trinity; they also do not believe that Jesus is son of God, they believe he was a prophet.
Right...our doctrine of Trinity means that we believe Christ is God! This belief is not shared with any other religion be it Islam, Judaism, Hinduism, etc. Many of the worlds religions will say nice things about Jesus (Islam for example). But only Christians bow the knee to him and confess with their tongues that he is God and should be worshipped as such.