A Game master is the person running the game. It is sometimes synonymous with Organizer, Larpwrite, Designer and/or Producer - however "game master" implies that the person is actually physically (or via for instance telepresence) present at the larp ("running things"), while a larpwrite, designer or producer might not even partake in the larp.
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 the fiction of the game during the running of a game. For instance by in-game mail or phone calls, or directing NPCs etc.
Non-diegetic Game Mastering
Affecting the game by breaking the fiction in some way.
A person whom is directly directing the action of a game by cutting the game or giving impulses and Narrative Voice Overs, usually in a black box, Freeform or Jeepform game, can be called Director, Narrator, Game master (or GM) or Facilitator.