RULE OF THIRDS
A commercial photographer takes photos for advertisements. They are usually hired by a company to take photos of their product. An example of this, is a Stock Photographer.
Fine Arts Photography are photos displayed in art galleries. They are often projects and are very personal to said person.
This is the photos or reports you see in the news. They are often hired by news, magazines, or newspaper company's to take photos of recent events.
These are the photographers on sets of movies, they document what happens during the filming processes. They are usually hired by the film director.