To actually give my opinion, I think "musician" is a general title meant to encompass the more specific types of musician. Where you have performers, composers, etc., these all require a particular skill set that is common to most, if not all, musicians. While you can be any of these things, you can be considered a musician... BUT... simply as a general term that everyone can understand.
If you wanted the term to be an actual professional title, then you would term it "professional musician".
I really don't think it's necessary to argue whether the general term of musician is correct for computer composers, as many of those people have the very same skill sets and abilities as performing musicians. Many of them might actually do so in their spare time. So I think it's unnecessary to try and differentiate between them. Call them musicians and call it a day.
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