Usually a one year internship follows or may be integrated into the program. While all licensed psychologists will have the same core areas of training, there is some variation in the amount of time spent in training on the specific skills used in the evaluation and treatment of mental health problems. Psychologists trained in clinical psychology are the most directly trained to work with mental health problems, but those with other training are also qualified, often by virtue of clinical internships, by specialty post-doctoral training or by years of supervised experience. A few states still license psychologists with only masters degrees, but in most states a licensed psychologist must have a doctoral degree. It is important that you ask about these issues if they make a difference for you.
Social workers train specifically in the tradition of social work.
After college they go to two or three year programs to get a masters degree, usually an MSW, in social work. The designation LCSW means licensed clinical social worker, and in most states this is the degree that insurance companies recognize. Often social workers must work under supervision for as many as four years after their training to achieve this level of licensure. Again, if you have concerns about these issues, ask. However the credentials and training of people in these categories is not as consistent between states and they are less likely to qualify for insurance reimbursement.