In Australia we use the word 'psychologist' rather than therapist.

A psychologist is someone who studies the human mind. This does not necessarily mean that they treat patients. They probably do research, write papers, work as advisors, etc. A therapist is someone who offers any kind of therapy (not just psychotherapy). However, if you told a friend 'I'm seeing a therapist', it would be assumed you meant a psychotherapist unless other information was offered. Shrink is a slang term for a psychiatrist (a medical doctor specialising in the mind), psychoanalyst or psychotherapist. I would say that 'therapist' is the most commonly used term.