A composer on the other hand is a person who sets a song to music. In short it can be said that a composer gives life to a piece of lyric or a song written by the lyricist. There has been a debate going on whether a composer should necessarily be a musician as well. A composer is supposed to know the nuances of music and should have studied music at a higher level.
On the other hand a composer need not be a professional singer or an instrumentalist for that matter. Many composers are adept in playing instruments such as the piano or the harmonium. They use these instruments primarily to compose music.
A musician has to study the basics of music and should be adept in playing instruments or singing if he or she has to establish as a professional musician. It is interesting to know that musicians can be composers too. There are several instances of musicians turning into composers. On the other hand a specialist composer turning into an established and a professional musician is not frequently seen.
A musician gets trained under a teacher initially and then either follows the style of the teacher or invents his own style of singing. He performs for the audience. He is a paid entertainer.
On the other hand a composer is employed by the film or the movie industry to compose music for a film or a movie. His job is to compose music for the storyline of the film as according to the various situations of the movie. He works in unison with the other workers of the unit such as the director, the producer, the story writer, the editor and the like.
The composer of the music for a particular film or movie picks the musician to sing songs for the movie. The musician sings the songs set to music by the composer for the movie.