I think it helps to clarify the difference between a dancer acting professionally and a dancer who belly dancing is her/his profession.

Asking, listening, learning, and caring about your behavior and influence on the greater community of belly dancers and how the art form is being presented to the public is a huge part of acting/being professional. But does a student who acts professionally a “professional dancer”? Now we get into titles, which are important in communicating where a dancer is at, what she/he offers and what can be safely expected of them. I “professional performer” and a Professional instructor” (a dancer being one does not necessarily mean that he/she is the other) is expected to be able to deliver certain services at a certain level. A “professional dancer” has to act with professionalism in ALL her business dealings, or he/she will not be very successful. A hobbyist dancer can be doing it for the pleasure and joy of it, a “professional” is providing a professional service. 
I would get into the issues of payment and part/full time in another post. ..
Just like any other business 85% of the time and work that goes in to a “professional” performer and/or instructor is administrative and not even directly dance related-things like advertisements, promotions, website maintenance, negotiating payment contracts and talking with clients about their needs and wants, answering students concerns and questions, cleaning the studio, buying toilet paper for the studio (my god how much TP can these people go through…) and water (oh that is why)… keeping track of your financials, paying taxes and then the other 15% training and performing, the pay dirt, the part we all like. Also the expectations for a professional dancer are higher, not to say that some dancers aren’t Divas, but the same behavior from a student dancer is easily forgiven as inexperience and “being a little too big for your britches” , will be seen as bitchiness and Diva-ness in a dancer who is calling herself a “professional dancer”, and will not be easily forgotten or forgiven. So a working professional better be on her best behavior ALL the time, and with EVERYONE. There are definitely different advantages to being a “professional dancer” and for being a professionally acting hobbyist dancer . Both of them get to dance with joy, and both of them deserve respect.
I know I used “she” more then “he” in this post, but please know I am referring to either gender:)

Here are some other great articles written by amazing dancers on this subject: