A Game master is the person running the game. It is sometimes synonymous with Organizer, Larpwrite, Designer and/or Producer.
Runtime Game Mastering
A game master that actively affect the game during the run of it. This can be done in several ways.
Diegeting Game Mastering
Affecting the game by introducing story elements in to teh fiction of the game during the runing of a game. For instance by in-game mail or phone calls.
Non-diegetic Game Mastering
Affecting the game by braking the fiction in some kind.
A person whom is directly directing the action of a game by cutting the game or giving impulses, usually in a black box, Freeform or Jeepform game, can be called Director, Game master (or GM) or Facilitator.