I can write a poem in my head without ever writing it down on paper. I still wrote a poem, even if I just pass it along orally.
If I write a song for my girl, I'm not going to hand her a piece of paper with sheet music and lyrics, I'm going to perform it for her. I may write it down, or I may not.
Of course, composed is a more precise word, but everyone still knows what I mean if I replace it with write.
I can write a poem in my head without ever writing it down on paper. I still wrote a poem, even if I just pass it along orally.
If I write a song for my girl, I'm not going to hand her a piece of paper with sheet music and lyrics, I'm going to perform it for her. I may write it down, or I may not.
Of course, composed is a more precise word, but everyone still knows what I mean if I replace it with write.