Counseling is a more short term or spaced out treatment for families, couples or individuals who want to work on a few things.

Psychotherapy ("healing of the soul") is a dedicated time for you to be listened to and understood deeply so that you can take back your story from the unconscious/unsatisfying patterns of believing and relating that hold you back. 

Psychoanalysis is like psychotherapy only more. People seek analysis ("soul examination") to relate better, heal from trauma and deep hurts as well as to liberate from persistent but hidden things that block them from living a satisfying life.