You see, all those Greek words, made up by people who were not Greeks at a time when creating "new" Greek words was fashionable, are more or less opaque for whomever does not have much familiarity with the so called Psi world. They are compound terms, sharing the first bit, "psych-" (which comes from Psyche, i.e. Soul.)
So, we have:
- Psychiatrist < Psychiatry < psyche + iatreia, ‘cure’.
- Psychologist < Psychology < psyche + logos, 'discourse, study'
- Psychotherapist < Psychotherapy < psyche + therapeia, 'nursing, cure'
- Psychoanalyst < Psychoanalysis < psyche + analysis, 'separation into components, close examination'
All this is very interesting, but did not answer the question. What's the difference?