I think this is a great thread and a good question.

I'm not a musician, (though I've been a singer and can play the guitar a bit) but my brother is, and some of my friends certainly are, so I can relate to this via my own "art" as it were, of theatre.

To consider oneself an actor to me is much the same thing. It certainly does begin with one's own perceptions of him/herself, and then is added onto by the amount of work put towards learning one's craft. I do think there is natural talent, but those who are privileged to have such a thing would do well not to rely on it, and most wouldn't because of their love of it, and their desire to learn whatever might enhance their joy of it.

The last, but not least aspect has got to be the audience. For actors, this is essential, as it's not a craft one can perform without that element to complete it. This is not the case with many other arts-one can write, paint, play an instrument and sing, dance, all on one's own, and take great satisfaction from just the doing of it.

But I can't think of anyone who would feel completely happy not being in a position of sharing what they love with others. Once this takes place though, then the element of judgement in the form of criticism (loving criticism from friends or relatives is wonderful and important to help provide a nurturing atmosphere) and I do think this can be extremely important, especially if the criticism comes from those one respects who are also experienced in the same art.

So for me, a musician who calls him/herself one-thinks, acts, and performs with love and respect of the craft.