Social worker - minimum of Bachelor's degree, sometimes/often Masters (MSW). Many therapists stop after this point, so there are plenty of social workers with decades of experience.
Psychologist - PhD (about 7 years after Bachelors, including a dissertation and extensive coursework and supervised counseling experience)
Psychiatrist - MD, authorized to prescribe medication. A small number also will do therapy; most focus on medication management

What does this all mean? Psychologists have more training and education, which sometimes means that they are better equipped to be therapists to people with mental illness. Social workers tend to have less training, depending on where they are in their career. For me, someone with 2 mental illnesses, it's important that I see a psychologist and one with years of experience. In terms of money, with insurance the copay might be slightly higher for PhDs.