It's not about gear, training, techniques or skill. A well-heeled amateur may have more and better equipment and be more technically adept than a working pro. An amateur may gather an immense amount of experience, either through years of work or through volume. Many amateurs are more artistically inclined and have a clearer "voice" than a lot of working pros. In this respect, you can treat most fine art photographers as "amateurs with exposure" -- they aren't doing the daily grind, and frankly any financial success they have is applause for effort they've done to please themselves.
It's about attitude and commitment. A pro will, within reason, get the customer's shot regardless of his or her technical or artistic reservations. The amateur is guided by his or her own interests, and can forego that architectural shot that's going to wind up badly distorted because it requires a stupidly wide-angled lens from an awkward position. He/she can choose the subject of a portrait and the representation of that person in the finished work. A pro needs to make the bride feel beautiful even if he's thinking beached whale so that he can make her look beautiful. It doesn't mean stepping outside of your ethical bounds or taking on jobs that would muddy your brand, but it does mean making the best sort of silk-looking purse you can out of some pretty badly-chewed sows' ears sometimes. It was beyond me -- I could do the technically difficult, but I couldn't pretend beauty, elegance or strength were there when I couldn't see it, and that's all in a day's work until you have enough credibility and reputation to choose your clients.