I think there are styles within these styles.
Sure. A module like White Plume Mountain, for instance, is clearly written with the "wargaming" style in mind, but important parts of it are not about the mechanics but about free roleplaying grounded in the PCs' fictional positioning (eg taking the doors of their hinges to surf down the frictionless corridor over the super-tetanus pits).
Are you interpreting “storyteller” as being a single, predestined storyline that all around the table are dedicated to acting out and moving to resolution (I hate to use “railroad as it’s a loaded term), with indie being lots of possible storylines, any one or more of which could resolve in any number of different ways?
I think that what [MENTION=205]TwoSix[/MENTION] has said upthread is pretty spot on. If you look at a module like Expedition to the Demonweb Pits, which utterly supposes that the players will take the GM's "hook" at various points and jump through portals, agree to work with shady characters, etc, the whole assumption is that the players are along for the GM's ride. (In this respect I find the module to be true to the ethos of earlier Planescape adventures like Dead Gods.)
I have more difficulty with indie style, however I read this almost as a cross between the two, where there is a story (or many stories) to be told, but they are dictated by action resolution mechanics.
The motto for the indie style could be "players hook GM" rather than "GM hooks players".
The action resolution mechanics should dictate outcome, but the GM should have framed the situation such that whatever happens, it will be both dramatic and thematically relevant.
Why is this called "Indie"? Is it just a reference to independent game companies, sort of like "alternative" music? If so, it needs a better name in my opinion.
Agreed. Storytelling and Wargaming are much more intuitive. Plus, Indie implies this approach could never possibly be in a mainstream game.
Well, on The Forge the technical label for what I'm calling the "indie" style is
narrativism, but that's a term which on ENworld gets used with a whole range of different meanings. The reason I used "indie" is because you're most likely to see this style put forward explicitly in indie-published games like HeroWars/Quest, Sorcerer, DitV, Burning Wheel, et al.
Is it possible in a mainstream game? Definitely, though certain traditional mechanical features of traditional fantasy RPGs can get in the way. Examples of that are coming up in the exchange between N'raac and [MENTION=85158]Dandu[/MENTION], as the resolution of the PC's attempt to capture a lizardfolk starts to turn on minutiae like precise density of foliage, and of trees near the village, and how many gnats are around, and how likely the fighter is to stumble into a lizardperson, and the wizard's encumbrance when teleporting etc. In the indie style, on the (I think fair) assumption that a lot of this doesn't have much thematic significance, there would be mechanical devices for compressing the minutiae while emphasising the dramatically significant stuff.
A mainstream RPG which is fairly well-suited to the indie style is 4e D&D. I think 3E has more of the mechanical obstacles that I mentioned, but that's not to say it would be hopeless.
These are the players who, as the campaign reaches its crescendo, interrupts the GM’s half completed description of the Master Villain twirling his moustache as he begins his monologue with “Enough flavour text – I waste him with my crossbow!”
By default, I would associate this with storytelling style. In indie play, by default there would not be a monologue - there would be an exchange between PCs and NPC, potentially engaging the action resolution mechanics depending on whether the exchange involved conflict.