It depends on what your personal definition of "professional" means. If it means someone who gets paid to do something then that's when you're a pro. If it means someone with the credentials like a resume or degree then that's when you're a pro.
To me, I think it has something to do with both but you don't necessarily have to get paid to be a pro. You can be at a pro level but still have a job outside of music. I know several guys that can flat out smoke on their instruments but yet still need a job to make ends meet. Me personally, I've been told I'm at a pro level, even though I criticize myself to death, but I still have to feed a wife and 2 kids, pay bills, and keep the cars running. I make a little money on the side from studio work or gigs but it doesn't pasy enough in my town. I wish it did. Actually, my goal is to go to school here soon, get a music degree, and maybe get a job either as a music director at a church somewhere or head to a bigger city and get more session work but right now my kids need food and gigs don't feed them enough.