The conversations are not entirely different. They're not different at all.
If the GM establishes elements of the shared fiction ahead of time, and does not reveal those elements to the players, then they act as constraints on action declaration. To reiterate an example that has been going on now for much of the thread, if (i) the GM has authored that the map is hidden in the kitchen rather than the study, and (ii) the players declare that their PC search the study for the map, then (iii) the players are not free to have that action declaration succeed, as the GM will (presumably) automatically declare, on the basis of his/her pre-established setting, that the map is not to be found in the study.
By that logic, the dice are also a limit on action declaration. Because if they declare they're searching the study for a map but roll poorly, it's not there. The players are
not free to have that action declaration succeed.
(You also make the pretty HUGE assumption that once the world has been pre-authored ahead of time that it's impossible to change. Which is not so. If the players are really focused on searching the study and not the kitchen or they roll fantastically well, perhaps the map just changes locations to reward them.)
This also assumes that the players look for what the GM planned. In this instance, the players might declare they're looking for notes and not a map, so the GM has to decide if those exist or not. Alternatively, even if they do look for a map in the wrong place, the GM doesn't have to give the players and easy win; instead they're challenged and encouraged to keep looking or think of something else that will get them to where they want to go.
Plus, one of my favourite types of story to write are investigations. Finding the killer, deducing why the ghost is restless, tracking down the monster, etc. Those stories fall flat if I don't work out the clues and details ahead of time. While they can shift as needed to keep the action moving, evidence shouldn't shift because the players declare an action. There's no challenge there. The challenge of the game is solving the crime and finding the criminal, or setting a trap and catching the monster.
How they solve things is dependant on them and their action declarations, but they still need to figure out who the bad guy in my notes is.
To say that the players have the "freedom to go wherever" is just to say that they can trigger different episodes of narration from the GM. It doesn't show that they have significant agency over the actual content of the shared fiction.
So?
Again, the players don't know what is a triggered episode or what is improvised unless they're looking over your screen. (Or, unless the DM has a tell like reciting their notes in a monotone voice or stalling and stammering as they improvise.)
This is why I did not frame the OP in terms of "improv" vs "prep", and have consistently explained why I don't see this as a very critical distinction for the purposes of this thread. The question I asked in the OP was about the GM establishing, in advance, the setting and backstory elements of the game.
This and your above statmente assumes the NARRATIVE is pre-made along with the world. Which is two different things.
Again, the campaign could be a giant sandbox set in the Realms where the entire setting and every location is pre-written and prepared, but the actual narrative and course taken by the players could be entirely driven by the players. Moreso, since they have access to the world lore as well and can decide to see places they like ("We need lore. Let's go to Candlekeep!)