If somebody can read music and play a musical instrument, if somebody can read music and sing, then either can be given the sheet music of a piece that they have never, ever seen or heard performed before and play, or sing, that piece exactly as the composer intended it to be heard. They have every right to call themselves musicians.

By this definition, my computer is a musician.

Composers and songwriters may interpret their own works differently each time they perform them. Putting the dots down in a score shouldn't necessarily preserve tunes in aspic.

In ensemble playing, sticking to what is written is advisable although it wouldn't preclude some well constructed ad-lib harmonies. Solo performances allow greater interpretation and the score may be no more than a guide.

My brother-in-law can sit down at a piano and make a good attempt at a previously unseen piece. Take the music away, however, and he is lost even if is a well known tune. I, on the other hand, can work out a tune from the score but would have to learn it bit by bit. If it is a familiar tune I can usually busk it on a range of different instruments. I consider both of us to be musicians.

Picking up on the original question, if a singer can present a song as a performance or work together with other singers or instrumentalists, then he/she is a musician.

DC