if the DM inserts elements in the moment, you are no longer dealing with discovering a shared world--you are discovering what's going on in the DMs head.
If the GM writes it up in advance, the players are discovering what went on in the GM's head. Either way, the players are discovering something about the GM's creation, and the GM is not discovering anything - s/he is inventing.
I'm not sure why, from the point of view of exploration, it matters to the players when the GM invented the material that the players are discovering.
The difference is that in the first one the world doesn't exist until the player and DM create it. In the second case, all the creating of the world has already been done.
You haven't explained why timing matters.
If the GM makes it all up on the spot, rather than in advance, it is no less exploration/discovery by the players.
One end of the spectrum:
The DM comes to the table with no world, no story, no statblocks.
One player says, "So my character is from a farm. Where do we..."
DM: The mud of the trail that you leave unconcernedly on your shoes as you enter the Hall of Lords contrasts with the emaculate dress of Lady Howenot, who turns and looks upon your character with disdain.
Player: Why am I here?
DM: That's for you to decide.
Player: "Fair lady, I'm searching for the Riddle of Mentios, perhaps you have heard of it?"
DM: "Are you from Mentios then? I had not thought a peasant from the land of milk cows and beans would have traveled so far only to muddy the elven-made floors of this hall."
<snip>
In this version, everything was made up on the fly by the player and DM.
Is this based on an actual play experience of yours?
Speaking from my own experience, it doesn't look much like any RPGing experience I've had. For instance, the GM is declaring important actions for the PC (eg leaving the trail of muddy footprints); and the distribution of backstory authority between GM and player seems quite unstable. The PC (and his/her players) also seems to lack some knowledge that s/he ought to have, such as how far s/he has travelled.
In my own experience, RPGing that is based on the GM making stuff up is supported by an allocation of roles between GM and player, and some structures to support that - eg the player sends various signals to the GM about the interests/inclinations/adventure desires of his/her PC (and thereby for him-/herself also); there are devices, formal or informal, for the player to introduce content into the shared fiction, etc.
world-features are defined by player/DM declaration on the spot, in response to what is happening at the time, to accomplish specific ends of the players/DMs. They aren't exploring a world, they are creating it.
The other end of the spectrum:
The DM is playing in his version of the the Forgotten Realms. He's made a few general changes, and filled in some details that published material doesn't include.
<snip>
Here the DM is taking everything straight out of Volo's Guide to the North, pages 140-142. That's what the inn is like, and the player gets to explore it in the moment, while the DM began exploring it when he read up on it before hand.
The GM is not exploring any bits that s/he made up.
There is also the oddity that the GM reads the book, and then the player listens to the GM channel bits-and-pieces of that book.
Ron Edwards wrote about this process:
Setting therefore becomes a one-step removed education and appreciation project. There’s a big book about the setting. The GM reads the book. Then, the players enjoy the setting, or rather enjoy the GM’s enjoyment of the setting, by using play as a proxy. As one text puts it, the GM is the lens through which the players see the setting. . . .
This kind of play is often called setting-heavy, but as I see it, when playing in this fashion, the goal of having the players enjoy the setting as such is actually at considerable risk. It’s hard to parse the relationship between (1) the story, first as created, then as played; and (2) the setting both as a source for conflicts (“adventures”) and something which might be changed by them. . . . in a way, setting is “everything” for such play in the GM’s mind, but “nothing” for play in the players’. Perhaps this is what leads to those monstrous textual setting histories in the books, with the only people who read them (or care) being their authors and the GMs.
The GM's creative choices (eg which pages of Volo's Guide catch his/her eye) make a big difference to which bits of the world the players actually get to explore via their PCs.
The key element is that with exploration, you are discovering and interacting with a third entity--the world. You and DM visit the world. With creation, you are interacting with the DM's response to your own immediate choices. You visit the DM's creative thoughts.
<snip>
A premade story is part of the world, so it is explored during play.
"The world" is not a self-subsisting entity. It needs to be authored. If the GM authors it, the players visit his/her creative thoughts - perhaps those of yesterday, rather than today. If the game uses FR, the group instead visits Ed Greenwood's creative thoughts. But someone had to create it. It didn't write itself!
And whether that authoring happens now or already happened, it may have been motivated by an author's sense of story telling. You don't escape exploration of an author's story motivations by buying the story that Ed wrote, rather than having the GM make up the world as s/he goes along. (As you put it in relation to Gygax's city encounter table, "you might say that it is a pre-established element of the world that exciting dangers are going to be there for the PCs." That is a story motivation, and not less of one because it has already been written down in the DMG. I have seen RPG worlds largely devoid of story motivations, but not in D&D products but rather Rolemaster ones)
I had to create some backstory for the Spectator. All of it was created to logically fit the lore given for Spectators in the MM, and the backstory of the mine in the adventure--none of it was created based on what I thought would lead a story in a certain direction.
<snip>
I created the architecture of the temple, the personality and name of the priest, and a variety of details entirely on the fly, informed by the details already established about the world.
<snip>
Exploration where the players interact with pre-established elements of the world as a third entity (including appropriate random tables to fill in details) and in the moment content creation is primarily to fill in fine details (not the same as pre-established material for the purpose of a fair challenge), is a significantly different experience than one in which the world is created by DM and/or players on the fly to fulfill story desires.
I don't understand why, in your final paragraph of this quote, you confine yourself to two of the four possible options you carve out. The pre-authorship can be driven by story considerations (I mentioned several modules upthread that exemplify this, and will add some more: Dead Gods, most Ravenlofte adventures, etc).
Or, as per the examples you gave that I quoted, spontaneous authorship need not be driven by the GM's story motivations, but by other considerations.
In other words, I don't feel that you've explained why timing matters, and your actual play examples seem to show that timing doesn't matter!
There are plenty of us who feel that it matters. There's nothing wrong with not appreciating that difference, but it's kind of annoying to us to be told that it doesn't matter, when it clearly does.
I know there are plenty of players who care if the GM made it up yesterday and wrote it down, or makes it up now. I am doubting, though, that the difference can be that one involves creation and the other doesn't, when in both cases the GM is clearly authoring. I am also denying that, just because the GM makes it up today rather than yesterday, that means the players aren't exploring and/or discovering.
I can think of possible differences, and [MENTION=996]Tony Vargas[/MENTION] has pointed to some. But, as I also posted, I think there is a degree of sheer legacy: because pre-authorship was important to Gygaxian play (and especially the way it rations information as part of skilled play), it has been assumed to be important to D&D in general.
Another difference may be that players are more interested in Ed Greenwood's ideas than their GMs'.
if the random roll determines that the player doesn't know the significance of the item, they might want to try to find out the significance. This allows them to explore and interact with the world in a different way than if they had simply had it handed to them--which would be interacting with a DM motivation rather than with the world as a third entity.
If it's good for the players to explore and interact with the world, then why give the roll at all? Just declare that the PCs don't recognise the holy symbol.
This is the same question I asked [MENTION=22424]delericho[/MENTION] - if something is a good play experience, why are we making a random roll to skip over it?