Station supervisors are responsible for the day to day running of sections or the entirety of a space station. In Startopia the player takes the role of a supervisor, often competing with or fighting other supervisors for visitors and sections in the process. They are responsible for placing buildings, hiring the workforce and other duties.
It seems there is some overlap between station supervisor and station administrator. It is possible that a station administrator runs an entire station, while a station supervisor runs a section of a station.