For me, scrum masters have always been regular members of the team who had the added responsible of organizing the meta-scrum aspects of the work. They scheduled the planning, retro, etc meetings as well as set up the task board once work was decided upon. They made sure meetings and stand-ups were running smoothly and stayed on point.

I could see where a person whose entire job description was "scrum master" would seem superfluous, but I have yet to work somewhere where that was the case.