By definition, a "professional" in any field is one who undertakes a specialized task and completes it for monetary compensation. A professional photographer is exactly the same. In my definition, if you are hired by clients to take pictures for them, and are paid money to do it, you are a professional photographer. However, since there are so people who are part-time professional photographers, and full-time professionals in some other industry, I've always used the terms, "semi-pro" to denote those people who are paid shooters for a client, but don't do it full-time...yet (I would fall into that category), and "full-time pro" to denote those who make their full living off of their photography work.
Both types of people can rightfully call themselves professional photographers. The only purposes for trying to limit the definition to only full-time pros are either arrogance, self-promotion or (worse) a desire to deprive people of a title they're rightfully earned by being paid for their work.