A canine behaviorist handles those canine problems that can seem to defy explanation. It's sort of like a canine psychologist. That's an exaggeration, but it's the type of problems a behaviorist might encounter. Unexplained and unprovoked aggression is also an area where behaviorist are found. A top level canine behaviorist will often be a veterinarian working at a major hospital.
Most behaviorists are trainers with a boatload of experience.
But be very careful when someone calls themselves a behaviorists, because the price tag for their services is going to be very high. Make sure you get what you are paying for. Some states have begun to license behaviorists.