Anyone who gives counsel can be called a counselor. Perhaps you mean a mental health counselor? If so, Onemandog's answer is pretty much right. A mental health counselor is usually trained to deal with one specific kind (or range) of problem; for example, a substance abuse counselor. A clinical psychologist (one who provides psychological counseling or therapy) has broader and more extensive education, and a higher level of credentials (degree and license). But not all psychologists are clinical; some teach, do research, design policies, etc.
Psychologists have a different "deggree", more training / school that is supposed to teach them to "look allittle deeper" so to speak. A counselor may, (or may not in some cases) be trained to "listen", maybe give advice and just evaluate whether you just need someone to talk to and try and help you, or if you are really in a bad way and can refer you to someone who is more qualified.
Pyschologist can prescribe medications & counselors cannot. Pyschologists also go deeper into your problems while counselors just scrape the surface. I've been to both.
Psychologist is in d mind while counselors looks deeper in the heart.