Good heavens.
Beginner should be fairly self-explanatory. Throughout the whole process there's no hard and fast dividing lines; I stopped thinking of myself as a beginner when I realised I was familiar with the territory of card magic; terminology, techniques, history, well-known effects and so on. When I see that a trick is a variation of Marlo's "Miracle Aces" and I know what to expect, that makes me feel that I have moved beyond "a beginner".
Amateur comes from the French and means simply "to love". If you are passionate about your magic, you are, in the most literal sense of the word, an amateur. This covers everything from beginner to professional in my book! A more helpful term might be "intermediate". I think that it's in this phase that you really find your feet in magic, when you start to select tricks that work for you, that appeal and suit your style. You build a repertoire and practise it.
Professional is typically used to describe someone who earns money from *whatever*. Also associated with those who have a qualification in *whatever*. So if you're out there performing for money, you're a professional magician. If it's not a primary source of income, perhaps you may be more comfortable with the term "semi-professional", but I wouldn't put it on my advertising. I work through an agent and take every gig I get, which isn't enough to earn a living, so I rely on my other streams of income as well. However, my clients get a professional service so that's how I market myself.
By the by, I make a distinction between professional magicians (paid performers) and professional creators (people who make and sell magic tricks). There are those who do both, but more and more there appears to be a clear divide and I think it's important to acknowledge that, especially with the trend towards attempted creativity this situation has produced.
There's another category; celebrity. Well known to the population in general. There's industry celebrities (Dai Vernon is a prime example that we can all get behind) and then the real big cheeses - David Copperfield, Paul Daniels, David Blaine, Criss Angel (although less so in the UK), Penn and Teller, Houdini...the guys that everyone has heard of.
It's worth noting that being a professional doesn't necessarily mean being "good". I've seen quite a few wince-worthy attempts by professional magicians, but that doesn't make them anything other than what they are.
