In my humble opinion, a professional is someone that does much more than just make a living from what they are doing. I do, of course, believe they should be paid, and that what they are doing as a "profession" should be considered their main "job," however, I think it goes much beyond that as well.
I think there are two main understandings of the word professional. For instance, if you say someone is a professional (insert something here) that usually means they make their living doing that. But what about when someone is describing someone else and they say "So and so is a TRUE professional." What does that mean? I think the distinction is that a TRUE professional, in addition to making a living at what they are doing, is also constantly seeking to better themselves in what they do, to improve their abilities, and to continue to strive to educate themselves about the profession they have chosen. For example, medical doctors are constantly going to seminars about their specialties and getting as much education as possible, military members are constantly training and studying to better themselves and make them more combat ready, to include academic studies of their "art", educators have to maintain annual training requirements, etc.
According to some theories, such as one I remembering having to study while at Squadron Officer School as an Air Force officer, in order to be a "professional" you have to have an academic background in whatever career you are in. For instance, doctors, lawyers, accountants, educators, etc. Notice a theme? They all have academic backgrounds relating to what they are doing. DON'T FLAME ME!!! I didn't say I agree with that (for instance, I know many military NCOs that I consider to be "true" professionals, but according to some, without the academic background, you are "in" the profession, but not "a" professional.)
In my opinion, a professional martial arts instructor makes a living from teaching martial arts, but a TRUE professional martial arts instructor not only does that, but is constantly seeking more knowledge about his or her art and about how they can become a better isntructor, dojo/business manager, etc. In other words, continually seeking to improve themselves and their ability to teach martial arts or manage their martial arts business. This, in my opinion, also includes helping others to improve doing the same, and, in general, "giving back" to the martial arts community as a whole.
If you are wondering whether or not you are a professional martial artist, ask yourself these questions (all in regards to your martial arts "profession"):
1. Do I make a living teaching martial arts?
2. What am I doing to improve my own abilities?
3. What am I doing to improve my ability to teach?
4. What am I doing to improve my abilities as a business manager?
5. What am I "giving back" to the martial arts community?
6. Am I constantly seeking to make myself, my students, and my school better?
7. Am I seeking out training as well as educational opportunities?
8. If I were a parent of one of my students, would I consider (myself) to be a TRUE professional?
Once again, just my opinion.