Function
The official mandate of any actor. This is formalised (like a job description).
Triangle of Change

Role
The part that someone tries to play. This is different from a position, which is accepted by others. People perform a role to acquire a corresponding position, but whether or not they get it depends on the outcome of the interaction.
Triangle of Change

Position
Position refers to the influence of an actor in the system, which is subject to acceptance by others. It is the result of the interaction process so far.
Triangle of Change