I've had threads on here about this and here is what I learned.
My own personal take is that you can't call yourself a professional anything unless it's something you make your living at. It's the tax return test. If it isn't what's on your tax return under "occupation" it is not your profession.
That being said, there are many here who mix it up with behavior. And that's quite a reasonable thing to do. You can behave in a professional manner, i.e. take it seriously and do all the things that show you take it very seriously as a craft, and play at a level that would get you paying gigs if that's what you wanted to chase after as a living.
Many people here will argue that this makes you a professional. I would quibble just a bit and say that it makes you pro-level in your attitude and abilities, but the word "profession" has a specific meaning. So when I say I used to play professionally that means something to you... it means I made my living in music. Otherwise the term "play professionally" has no meaning at all. It could mean almost anything.
You can be a teacher without gigs and be a professional musician if you are a music teacher. But if you are otherwise not putting "musician" on your tax return, you are not a professional musician.
My definition only (well, that and the dictionary

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