I will get more specific about the types a little later. Psychotherapy represents a relationship. Not a friendship or a work acquaintance, though there are common elements. In this important relationship you are exposed to a model of relationships that can be used outside the therapy. Psychotherapists are trained in the rules and techniques for their specific school of thought and use their skills to effect a change in the patient.
All relations have rules, and different relations have different rules.
For example the first relationship is the mother-child. As the child grows, the rules are modified. Ideally, early on the mother provides all that is needed and as the child grows and becomes more independent, the mother gives the child more autonomy. Finally at some point the child is no more and an independent person exits. These rules are not agreed upon but are inherent in the relationship.