The main difference between coaching and psychotherapy is the focus of the issue to be resolved.
Object of psychotherapie is the treatment of disorders of experience and behavior.
Psychotherapy is therefore needed if someone suffers from intense, uncontrollable emotions, such as excessive anxiety or depression.
Coaching, however, is based on the treatment of a specific problem. The term "coaching" comes from the American language use. A coach is actually a trainer who usually works with athletes, where he doesn't only look at the physical, but also the psychological aspects of training and competition. Typically the coaching, as it's understood nowadays in this country, is about overcoming professional problems and solving relationship conflicts. The professional problems could be about the solution of a bullying situation, about reaching special career goals or about planning a self-employment or the development of a special project. The own feelings can be seen only as a guideline: What situations solve what feelings? What rational formulated goals are also relevant on an emotional level?
Supervision is the advice of colleagues who work in a social profession and want to have a look at their behavior regarding clients and/or difficult cases. So it's a coaching in terms of the social profession and the interaction with clients. Supervision is available for virtually all social professions, e.g. doctors, (psycho-)therapists, teachers, coaches, trainers, kindergarten teachers, social workers and nursing professions.