Jim Carroll has got it right on this point. Success is not necessarily a financial thing, but respect is through mutual love of what you do.

I was in bands, many of which turned pro, and that normally triggered my leaving, as having a good job, mortgage, kids etc, the gig circuit didn't appeal in any way whatsoever. As it is, I enjoy what I do, look forward to getting the guitar / banjo / fiddle out and don't feel I have to "do this" in order to live. My old mates who turned pro always said they didn't enjoy it as much after the initial feeling of "made it."   

The real me, away from this silly non de plume, does appear to enjoy a degree of respect, and it is a wonderful feeling when people travel a distance because they heard I am at a club that night.

You couldn't begin to buy that respect.

Ditto many classical players. If I note they have interpreted a challenging composition and released it, I may go out and buy it, together with millions of others around the world. But are they famous? No. BUT they are successful and that is the wording of this thread.

Ditto many folk musicians. The difference being that their classical counterparts such as Andreas Scholl could, if they wished, drive a Rolls Royce into a swimming pool. Pure economics that though. The world market being much much larger....