This is why the text matters, best practices and GMing advice and all of that. It absolutely informs the way people play.
Suppose that a player declares (as their character) "I look for <X>". In typical D&D play, X could be a secret door in a seemingly dead-end wall, or an alchemist with a potion for sale, or a smith to reforge the broken magic-sword the PC has found, or a portal to another world, or any of a myriad of things that D&D adventurers hope to find to help them pursue their adventurous goals.
What do the rulebooks say about how a GM should respond to this action declaration?
Moldvay Basic says the following that's relevant (B3-B4, B21, B52-B53):
It is the DM's job to prepare the setting for each adventure before the game begins. . . . The dungeon is carefully mapped on paper . . . At the start of the game, the players enter the dungeon and the DM describes what the characters can see. . . . As details of the dungeon are revealed, the player characters will meet "monsters" which they will have to avoid, talk to, or fight. . . .
A secret door is any door that is hidden or concealed. . . . Any character has a 1 in 6 chance of finding a secret door . . . The DM should only check for finding a secret door if the player says that the character is searching for one and searching for in in the correct area. . . .
To "stock" a dungeon means to fill in the general details, such as monsters, treasure, and traps. Special monsters should first be placed in the appropriate room along with special treasures. The remaining rooms can be stocked as the GM wishes. . . . Besides the monsters which live in rooms, characters may encounter monsters which wander about the dungeon. . . . At the end of every 2 turns, the DM should check for Wandering Monsters. To do so, roll 1d6: a result of 1 indicates that the party will encounter a Wandering Monster in the next turn. . . . Wandering Monsters may be determined at random or selected by the DM.
There is an example of building a dungeon - both mapping and stocking on pages B55-B57. These reinforce the implications of the text I've quoted, that the GM's job is to do all this stuff as part of prep. And there is an example of play on pp B59-B60 that also makes some things clear: the example begins by saying that the PCs have "discovered the trap door in room 4" of the example dungeon. There are lots of examples of the players declaring "I look for <X>"-type actions:
We search for secret doors. We search for traps. We look for hidden compartments in the box. Is there any movement when I prod the rags with my sword? There are also lots of examples of the players declaring similar but more open-ended actions:
What do we see when we look down the corridors? Is the breeze strong enough to put out our torches? We listen at the door - what do we hear? Do we understand the voice? What does the room look like? it is pretty clear in all these cases that the GM is relying on their dungeon map and key, plus the wandering monster procedure, to resolve those action declarations. The second, open-ended category we might think of as invitations from the players to the GM to elaborate the framing of the scene. What's interesting is that the first, "I look for <X>" category also get treated somewhat similarly: the GM is entitled to elaborate the scene as including "You don't find any traps", for instance, based simply on their map and key, without that being anchored to any player-side action resolution process.
I'm not going to provide quotes from Gygax's AD&D rulebooks, but - unsurprisingly - they contain similar sort of material. The advice in the PHB on Successful Adventures takes as an obvious premise that a big part of playing the game is learning the contents of the GMs map and key. (It's not as clear as Moldvay - who on p B4 says "Eventually, the DM's map and the players' map will look more or less alike - but it's still pretty clear.) The DMG contains a sample dungeon, which like Moldvay's illustrates how the GM draws a map and then stocks the dungeon contents, including doors (both overt and secret), monsters, traps, etc. There is a discussion of listening at doors, and searching for secret doors, that is similar to Moldvay's. And there are rules for wandering monsters, discussed in the Introduction and in Appendix C.
The 4e rulebooks are not as clear as this. For instance, the following is a very good observation about skill challenges, posted by LostSoul on these boards a little over 9 years ago:
My guess is that skill challenges work better when they are resolving an abstract situation.
If you have all the details of the situation nailed down, then it's difficult to change those details based on the result of a skill check. You can't introduce a secret door, a wandering monster, or a frayed rope if you know there are none of those things before you start the challenge. That means you can't introduce those elements if the PC succeeds or fails on their check.
If the situation is abstract - and almost all social conflicts are abstract, since the DM can't possibly know all the details of an NPC's personality - then there's a lot of room for the DM to react to the skill checks of the PCs and prompt the players for more.
The abstract situation allows the DM to directly address the player's reason for playing the game, as telegraphed through their PC's actions and build. If the situation is too detailed to allow the DM to do that, then it fails.
But the rulebooks don't discuss this. Page 112 of the DMG is headed "Mapping the Site" and begins"Once you've come up with a concept for your adventure setting, you probably need a map" and it illustrates all the typical dungeon mapping symbols that when it was published went back 30 years and now go back 40. The next page (p 113) talks about "The Map Key" and gives advice to write up rooms basically the same as Moldvay's.
How is this approach to map-and-key to be used in resolving a skill challenge (say, to flee from pursuing monsters)? How does it fit with the advice about "saying 'yes'" found on p 28 of the DMG (and further elaborated in the DMG2):
As often as possible, take what the players give you and build on it. . . . Take it and weave it back into your story without railroading them into a fixed plotline.
For example, your characters are searching for a lich who has been sending wave after wave of minions at them. One of the players asks if the town they are in has a guild of wizards . . . [that] would have records or histories that mention this lich's activities in the past . . . That wasn't a possibility you'd anticipated, and you don't have anything prepared for it. . . .
Imagine you say there is a wizard's guild. You can select wizards' names from your prepared lists. You could pull together a skill challenge encounter . . . Instead of cutting off possibilities, you've made your campaign richer, and instead of frustrating your players, you've rewarded them for thinking in creative and unexpected ways.
In this respect, 4e is not so much incomplete as over-determined in an inconsistent fashion. It sets out two modes of resolving action declarations - map-and-key play, which centres the players triggering revelations from the GM's notes; and player-driven skill challenge-type play, which focuses on stakes and the success or failure of declared actions as the way of resolving "I look for <X>"-type actions.
I think the incoherence of 4e, especially when compared to the straightforwardness of the classic D&D texts, is an out-and-out weakness. It makes it harder to play the game. And I don't think pointing to "invisible rulebooks" really helps here, because for most RPGers those invisible rulebooks centre map-and-key resolution, given it's long tradition in RPGing.
A RPG which wants to offer a different approach from that tradition really needs to spell out its procedures. The two clearest examples I can think of are both Vincent Baker games: In A Wicked Age and Apocalypse World. As far as "I look for <X>-type actions", they have clear procedures in both cases (the former is consensual-with-GM-chairing/leading; the latter is based on a soft/hard move structure related in part to whether the basic move "Read a charged situation" is triggered).
But an interesting alternative to map-and-key resolution of "I look for <X>" dates all the way back to the earliest days of RPGing: 1977 Classic Traveller. Its Streetwise skill reads (Book 1 p 15):
The individual is acquainted with the ways of local subcultures (which tend to be the same every-where in human society), and thus is capable of dealing with strangers without alienating them. . . .
Close-knit sub-cultures (such as some portions of the lower classes, and trade groups such as workers, the underworld, etc) generally reject contact with strangers or unknown elements. Streetwise expertise allows contact for the purposes of obtaining information, hiring persons, purchasing contraband or stolen goods, etc.
The referee should set the throw required to obtain any item specified by the players (for example, the name of an official willing to issue licenses without hassle = 5+, the location of high quality guns at a low price = 9+). DMs based on streetwise should be allowed at +1 per level. No expertise DM = −5.
This is clear text. Though at odds with map-and-key-based invisible rulebooks. It would be interesting to see how different these discussions would be if the Traveller approach, rather than the classic D&D approach, had become predominant across the hobby.
