in all of these, the DM is still deciding what actually does happen in the world.
I think that addressing this issue is quite fundamental to distinguishing playstyles.
I want to talk about in relation to framing conflicts/narrating situation, and then in relation to action resolution.
In relation to the framing of conflicts, here are two examples from actual play:
* GMing a thieves-only Greyhawk campaign, I have the PCs discover that the Lady Mayoress of Critwall is a member of a Chemosh-worshipping cult (the session was over 25 years ago, so I'm hazy on the details);
* GMing my current 4e campaign, the PCs discover Orcus cultists working as kitchen hands for the Baron of Adakmi.
From these descriptions, you can't tell whether the game is player-driven or GM-driven. To learn that, you need additional information.
In the first episode, the reason that I, as GM, introduce that story element is because I've been reading my Dragonlance Adventures hardback, I like some of the flavour around Chemosh (roughly, the Orcus of the DL world), and so I introduce a Chemosh cult into the game. That's a GM-driven moment of play. I can't remember much about the Mayoress, but my best recollection is that she was only an element of the game because I had introduced her.
In the second episode, the reason that I, as GM, introduce the story element is because half the PCs in the campaign are Raven Queen cultist and hence diametrically opposed to Orcus. The importance of the PCs' relationship with the Baron was also something that the players had been pushing, as part of their emergence into paragon tier in the context of the town's political scene. That's a player-driven moment of play: although the GM is the one actually doing the job of framing the conflict, I am following the players' leads. I'm not inviting them to follow my leads.
I think any game in which the authority for framing conflicts and narrating transition resides with the GM (which is pretty much all mainstream RPGs, "indie" or otherwise) individual episodes of play may involve elements of both player and GM direction, and from episode to episode the balance may shift back and forth from one to the other. One reason for this is simply that the GM, in framing conflicts, has to introduce fictional content, and if s/he does that job well the players may find it interesting and end up building on it - thus generating a back-and-forth between GM and player contributions to the fiction as the game unfolds.
Turning now to action resolution. In some RPGs, the outcomes of action resolution are expressly binding on the GM. (I think this is the default for D&D combat, but not so much for D&D non-combat outside of 4e's skill challenges).
And in some RPGs, (i) part of action declaration is establishing the player's intent for his/her PC, and (ii) if the player succeeds on the check, then that intent is realised. (Burning Wheel is an instance of this, and I think D&D combat resolution is meant to work like this, at least as written.)
In this case, it is not the GM who decides what happens. It is the player. And that's another important aspect of a player-driven game: if the players can introduce content into the shared fiction (via actin resolution which is binding on the GM) then they can shape and constrain the story elements that are available to the GM in framing future conflicts.
Of course, if the GM were free to just introduce new story elements at will, then there would be no such shaping or constraint - but this just goes back to the first issue I addressed in this post, of where the material for framing conflicts comes from. If the GM is obliged (whether formally or informally) to have regard primarily to the player's signals in relation to introducing story elements in the framing of conflicts, then s/he is not free just to introduce new material in order to circumvent the outcomes of action resolution.
I've given some practical examples of this upthread, from my 4e game: with Torog dead, the Underdark
is erupting in chaos; with Lolth dead, her webs are not longer there to hold the cosmos together. I am not free just to introduce new material into the fiction (eg new gods, or powerful NPCs, or whatever) to circumvent these consequences of action resolution.
I'll finish with a slightly orthogonal point: this also illustrates how 4e can be both a combat-heavy game and a story-oriented game. If the NPCs and entities with whom the PCs are fighting play meaningful roles in the fiction, such that defeating them in combat matters to the state of the fiction, then there is no tension between the game being one in which combat between the PCs and these entities is prominent, and the game being one in which the fictional stakes are what drives the campaign onward.
(In my view, the main reason that classic hack-and-slash games are both perceived as, and experienced as, shallow is not because of the preponderance of combat, but rather because of the lack of meaningful stakes. Filler combats are the enemy of story, as well as an enemy of player-driven play.)