There are 3 major approaches in psychotherapy: psychoanalysis, humanistic, and cognitive/behavioural.

Psychoanalysis is ultimately based on Freud, but there have been many developments of his original theories over the decades. There are currently 10+ different approaches, all having developed Freud's ideas in one direction or another (ego psychology, Kleinian, Interpersonal, object relations, and others).

Humanistic psychotherapy is the one most people think of on here. It includes Rogerian (ie: client centred), Gestalt, psychodrama, transactional analysis, yalom's approach, and others.

The cognitive/behavioural approach focusses more on attitudes and beliefs (hence the term "cognitive"). It includes CBT (cognitive behavioural therapy), CAT (cognitive analytic therapy), and Rational Emotive Therapy, among others.

Transpersonal Psychology is often considered to be a 4th approach. It differs itself from the humanist approach because it includes spirituality. This is not as regards faith or any specific religion. Rather, it includes the natural spiritual hunger and striving in people. It seems to be a development of Jung's ideas. An example of this is Psychosynthesis.