There are three types of people. Psychiatrist, psychologist and social
worker.
Psychiatrist is a medical doctor with an MD. Psychiatrist prescribes
psychiatric medications, and usually does not do much counseling. There
are exceptions, but very rare nowadays and will be very expensive.
Psychologist is a specialist with a Ph.D. or Master that is trained to do
psychological testing and counseling. A typical example is cognitive
behavioral therapy.
Social worker is the lowest in psychiatric care. They do a number of
different things, and some of them do talk to and counsel patients. They
usually have the least amount of formal training, but some of them can be
really really good. They charge the least amount of money.
Most insurance will cover authorized psychiatrist visits. There is a
usually a limit on the number of psychological counseling services one can
have every year. The coverage varies from insurance to insurance.