Yeah, that's the distinction, I think... player-driven versus GM-driven. The example I gave of the Blades campaign is showing the agency that players have on the direction of play beyond just that of control of their characters. They have a strong say in what the game will actually entail. The world is sketched prior to play (Doskvol is a very detailed setting, but the way it is presented leaves a lot of area for input), and then fleshed out through play.
I think a game where a GM has a story to tell as you mention has more in common with one of these two types of play than the other. I don't think that what you and
@robertsconley are talking about is entirely GM driven. There is some amount of player input, for sure, and the GM may not have a story to tell. But the GM is still authoring the vast majority of what is available for play. That's the similarity that I see is key... that's what makes it GM driven in my mind.
For example, the players in my Mothership game were free to take whatever jobs they wanted. They could then go to any locations available to them, per their means. There were plenty of jobs on the station, and plenty of jobs off the station out in space or on other planets. But the nature of those jobs and the content included in those jobs? Entirely made by me. I was driving play in the sense that everything play was about was chosen by me.
My players had no issue with this. They understood the nature of the game, and they approached play accordingly. So I'm not using the descriptor "GM-driven" as a negative. It wasn't a railroad, it wasn't linear, I would still describe play as a sandbox type game. But the content of play is very much up to the GM rather than the players.