I write and I feel proficient in my ability to mesh with most other musicians, but I don't feel like I know a whole lot about theory. I know that the circle of fifths is a thing, but I couldn't tell you anything about it.
I think I know where the OP is coming from. It has nothing to do with theory or reading or whatever; and I'm not discounting that. I can read decently (although not like a horn player or other cats who were weened on charts), and I've got a decent grasp of theory (but I try to learn something new every day). But that's not the point.
What the OP is getting at is, a guitarist plays guitar. He's concerned with the instrument. A musician uses his instrument to play music. The music comes first. It's all about the music (or the song), not the instrument used to make it OR the guy playing it.
I don't want to sound all airy-fairy, but being a musician in the context of what I think the OP is getting at is about leaving your ego at the door and doing what is best for the song.
As I understand the OP, a musician is one who sees the big picture in a given piece. I play electric/acoustic/bass/some drums/enough keyboard to get into trouble and I know how to mix sound. I know how the bits fit together...though convincing people twice my age of that fact is another story entirely.