Let me see if I can get this straight.
What you're calling "map and key" basically means that the game world is made up of certain predetermined facts, and that a large portion of the game is about discovering these facts. These facts often refer to locations and their contents (the literal map and key) but can also refer to other things (like people, organizations and the relationship between them).
The alternative method, which I'm not sure has been named in this thread but I'll call it narrative, deals more with players establishing facts by themselves (even if that's not what happens in the fiction).
So to take a very simple example: there's something in a warehouse the PCs want. To get to it, the PCs want to find a way to avoid the warehouse's security. In traditional map-and-key play, the GM has prepared the warehouse ahead of time. There's a map, of course. They might have prepared guard patrol routes and if there's a backdoor or alternate entry, it's because the GM decided there should be. Depending on the game and what resources the PCs have available, they can discover these means, or figure out weaknesses in the patrol routes, or maybe even bypass these restrictions if they have enough resources (e.g. teleporting into the place).
But in the more narrative approach, the GM probably hasn't prepared the warehouse in any great detail, other than "there's a warehouse with a McGuffin" and "there are some goons guarding it." Any additional details would be, from a real-world perspective, created by the players' actions. A PC staking the place out would roll Perception (or spend some meta-currency), and on a good roll they would get to create a weakness in the place's security. Within the fiction of course, the weakness was always there, the PC just discovered it. But from the perspective of the players, the player's good roll was rewarded by the GM saying "What sort of weakness did you find?"
Am I understanding these ideas correctly?