I thought about this after two things. One of them was somebody saying they hated the term "Game Master" because it has "Master" in it. The other was comparing some of the campaigns I've been in.
Pretty much all of the campaigns I've done have fit into the following four categories:
1. Traditional. The Game Master determines the storyline. The dice are never fudged for drama, stats are more important than backgrounds. Dungeon crawls and the like are important and the GM often uses modules. Character death is considered a reasonable outcome, without the need for any "story" reason for it. Ultimately, the dice rule. Plot is paramount and character is often minimal.
2. Storyteller. The Game Master determines the storyline, but may over-rule the dice. There is almost always an overall plot or arc that the players are expected to follow. Character death is less common and the GM may fudge the dice to avoid it if it does not fit the plot. (Although some GMs believe the dice should never be fudged regardless of the style). The focus is on telling a good story, but the outline of the story is often already written. Plot comes before character, but character has an importance.
3. Troupe. The Game Master is a facilitator, but the overall storyline is determined by the players and their interactions. The players have real choices, and the GM is ready to rewrite the entire campaign (or send everyone to Riverworld, ahem) if needed. Character comes before plot, but the overall plot remains important.
4. Sandbox. The Game Master is purely a facilitator who sets the rules of the world. There is a setting, but often no overall plot. The characters are free to make their own choices within the world as defined, regardless of consequences. Character is paramount and plot is almost unimportant.
One interesting thought on this is that Traditional pretty much always takes place face to face, while Sandbox is very common online (the typical MUD, for example, is a Sandbox).
Thoughts? Am I missing anything?