Relating to photography, a professional is usually associated with making your living doing photography. Otherwise, perhaps you would be called a hobbyist or maybe semi-pro. By those definitions, I have been a professional photographer, semi-pro, and hobbyist over the years.
One definition of professional as a noun is a person competent or skilled in a particular activity. The definition of hobby is an activity done regularly in one's leisure time for pleasure - with no indication of skill level.
Based on these definitions I will always be a professional photographer due to my high level of skill and depth of experience. A professional people photographer must be more than that. It is also respecting your subjects or clients, being on time, being honest, doing the best job you are capable of doing, and keeping whatever promises you make. If you hire a photographer and he or she doesn't do all these things, then you've hired someone who is not, strictly speaking, a professional photographer regardless of how much money they make or their skill level.
For example, a recent viral family portrait, which was shot by someone who considered herself a "professional" photographer, looked like the ones in this LINK. You can see a few of the photos below.
Someone who is truly a professional photographer would have understood lighting enough to know how to use light modifiers, outdoor flash, or just to move the family into the shade, and would have known where in the shade would have been best. The family was charged $250 for the photos. I'm wondering if the photographer ended up giving a refund for these once in a lifetime (literally) photos.
Here is a shot I did under the same lighting conditions (midday sun), but with a light modifier (a diffuser or scrim):
A professional photographer should give you the photos that you want and love. If the photographer can't do that, or if the client isn't happy with the results and do not want or like them, they shouldn't have to pay a single penny for them. Most photographers charge a "sitting fee" or a "creation fee" and they won't refund this fee. A few might offer a reshoot and even fewer a refund. Better would be to not have to pay a fee up front, just pay for the photos you want. Perhaps a session appointment fee which would be refunded at the appointment. I know of one photographer who just takes the client's credit card but won't charge anything on it unless the client doesn't show up which is in their contract. His average sale is in the many thousands of dollars - no creation fee needed.