I don't think those two things are equivalent, and I think the first is not sufficient for the second.
In almost any RPGing, a player action declaration for their PC will affect and change the game world. It means that the world now contains a character doing, or at least attempting, whatever the player declared. And often it will also prompt the GM to narrate something to the player about what happens - perhaps by reading from their notes, perhaps by extrapolating from their notes, perhaps by just making something up.
But if the player was just, in effect, offering blind prompts to the GM, then I don't think the player acted with much agency or made very meaningful choices.
For me the classic critique of blind prompts, from the perspective of player agency, is found in Lewis Pulsipher's essays in late-70s/early-80s White Dwarf. His focus was on what he called "lottery D&D" - where the players have their PCs draw from Decks of Many Things, pull levers, drink from wells in the dungeon, etc, and the GM reads from their notes or rolls on their chart to tell the players what happens. He contrasted this with what he called "wargame-style D&D", which is more or less Gygax/Moldvay-style dungeon-crawling, based around the players gathering information about a somewhat static GM-authored situation, and then acting in a planned, reasoned way on that information.
I think Pulsipher's critique of lottery D&D generalises to play where the flavour/colour of the play is less gonzo than drinking from a magic well, but the structure of play is the same. And a situation in which the players know that some indeterminate badness will happen if they don't get from A to B in time; that one path to B is short but dangerous; and that the the other path is longer but safer; has the underlying structure of "lottery D&D". The players have no real choice but to declare their PCs leave A for B; and they can either pull the "maybe this will help us" lever, of taking the short route, or they can leave the lever unpulled and find out what the GM's default narration is by taking the long route. It's all very colourful, and in some fashion it "affects and changes the game world", just like pulling levers in lottery D&D does; but the choices don't seem meaningful to me beyond being gambles. And I don't see much player agency.