Guitarist or musician?
From my point of view, a musician is someone who makes music. It's that simple.
I used to make the guitarist/musician distinction, calling myself "just" a guitarist. But once I realized that I (a) have a style all my own, and (b) can hang with good "musicians" in a lot of different situations - not all of which match my style - then I started calling myself a musician.
If you look at music as a form of communication among musicians, then there are two important skills to have. First, you have to be able to play with other musicians. You have to hear what they're doing, anticipate where they may be going, and respond as appropriate. Second, you have to be able to talk to other musicians. This doesn't require a deep knowledge of theory, but you should be able to name the notes you're playing, have an ability to name chords, and anything else that helps to communicate verbally within the framwork of the kind of music you're playing. Obviously, the demands are going to be higher for some genres (e.g. jazz) than others (e.g. blues).