Oh and this is mostly about older D&D.
Oh, this might be boring. I'm sorry if it is.
In short, maps and keys and everything else you determine ahead of time are things that are true about the game world. Possibilities, segregated into charts are things that could be true about the game world.
B/Maps, Keys, Worldbuilding and Good Facts
I once spent weeks drawing a world map (lovingly adapted from a map of South America, turned on its side), prepping details, fleshing out NPCs and the back histories of notable rulers for a game that lasted only a few sessions. The world, its details, its NPCs were boring for the players. They wanted to go into a dungeon and take stuff and fight monsters, not explore a far-future fantasy Brazil. I was fourteen and I had just learned that (a) the only good fact about a game world is the fact used at the table and (b) that I, as the GM, don't get to determine what constituted a good fact, I just get to think up what might be good facts.*
At its most basic, the facts of a world in older D&D are largely just the maps and the keys that describe it.** You don't need to describe agriculture or exports and you don't need to know who is sleeping with who. If the king of X is at war with the king of Y then you only need to know about it when it shows up in a key entry where one of the guards is a spy for Y and desperately wants out. You probably don't need to know anything about Y or the kings or anything else, even then:
The spy approaches the characters after they've been rebuffed from the gates and says, "look, I can get you into the castle if you can get me across the border to my sick mother, no questions asked" and that's all you need and that's older D&D and its beautiful to see and engage in.
C/Tables, Charts, Vornheim
But then the players decide they no longer trust the spy and threaten torture or to leave the spy bound and exposed on the plains, half way to "mom" until they get more info. So there is probably a chart for that: why X fights Y, why a spy serves a country.*** You can roll on Morale to determine when the spy breaks and use charisma checks to make “attacks” on the spy's Morale score. It's a do-able situation without a much work, but the tricky work of being a GM is figuring out how to react to that kind of stuff each time it happens not because it happens sometimes, but because tt happens, a lot (especially outside of dungeons, a point in the favor of dungeons) and no matter how creative you are, details start to repeat (which can be fun and a thing in and of itself).
So if maps and keys are facts about the game world, tables and charts describe either tenant/contingent, player-facing facts (facts about the physics of the game like, “what conditions, if any, do I have to satisfy to control/be a character of type x, of power level y with attending fact z?”) or possible facts.
It's easier to talk about this with examples.
Moldvay Basic (B8)
Tables organize information by giving it a set direction. All the values in a single column have the same relative weight and all the values across a single row have the same relative weight. Progression, if progression occurs, occurs in a set direction (in the caption from Basic, it occurs down and from left to right, though the latter progression feels less deliberate). (tables like this are usually fast per Zak's schema).
You can add sub-options within a table by adding (nesting) another table within the first, as in the above caption (Table Lvl 1: Describe what you see about the book from the most cursory glance (It's on Mathematics OR It's in a Foreign Language) -> Table Lvl 2: Describe what you see if you look in greater detail). For every additional table you nest, you add one more node/articulation point. I've never used a table with more than one level of nesting that was worth the work to try and use at the table.
Which is to say, nested tables work great when they're not meant to be all the information, at once. This usually means they're built around the way play works/the way players ask information:
Table lvl 1
I take a book off the shelf, what is it?(GM rolls)You don't know, it's in a foreign language.
Table lvl 2
What language?(GM rolls again)Goblin
recursive back to Table lvl 1
OK I hand it to my Goblin retainer and ask him what it's about.(GM rolls again)Mathematics
This result, for reasons having to do with surprise and the joy of watching something being created/discovered and of creating/discovering something together, is like exponentially better than a table with a, “Book on Mathematics, in Goblin” in it.
To put it more concretely: when you are rolling on a table like this, the player knows what you are doing; they are pushing a button in the game and you are turning the machine's crank and reading out the result. Which is to say, it is something they are doing and it feels like they're doing it and and it feels like they are doing it with you and it feels like the end result is something you worked together to create. If the end result happens to be bonkers or cool (and a good table helps encourage these kinds of results) then you've created something bonkers and cool that was not heretofore in existence which makes it even more funny or cool and, likely, memorable.
I do find nesting tables otherwise awkward in play (rolling, squinting at paper, finding the next die, rolling again, interpreting result, etc).***
Vornheim (46, stolen from Brendan's blog)
Charts, on the other hand, describe a more complex relationship between data where data is not necessarily of the same relative weight and the information moves only in a suggested or implied direction (you could say that a chart is cyclical and/or undirected).
Charts are a way of providing possibly related information that doesn't need to be constrained by a direction. I'd suggest that when you are describing variable outcomes that don't have to do with the physics of the game and have various levels of useful information to return, a chart is always the way to go.
You can also break the direction of a table such that it feels like a chart. Here is one Gus made at the bottom if his post here.
Vornheim has really good charts and is easily found so I'm sticking with that for examples. If you look through Vornheim's Aristocrats chart you'll note, progressing from left to right the columns read):
i. Given name
ii. Family name
iv. A social fact (what others might say about the character)
v. A psychical or behavioural fact (something the players will notice when interacting with them)
vi. A relationship (relates the NPC to some other NPC on the chart)
The information is in the order in which the GM needs it. Even the other facts narrow from what the players might hear about the NPC from anyone to what the players would know from seeing the NPC (or talking with someone who had).
Game, tell me about this aristocrat, what is it's name?LeopoldI need more.Von VorgWhat should I know about it to use it in play?It's secretly a lichWhat else? (the players are asking about them or racking their characters' brains to recall a useful detail)*Its a trade magnate, famous for partiesWhat else? (the players have tracked them down)It always wears furs, walks a displacer beast.What else? (the players are getting involved in their private lives)It's engaged to... (GM starts over again)
BUT ALSO YOU CAN BREAK THE ABOVE AT ANY POINT (LET'S SAY THE ASTERISK) AND REPEAT QUESTIONS AT ANY USEFUL LEVEL
What else? Is a philanderer. What else? Has spent thousands on diamonds recently.
This is a whole game you can play with the players together. The designer has defined its outer limits, but you two are working things out together and neither of your know the outcome. With a nested table, at least, you can sort of see where things may head. With a chart, there is a much better chance of surprising the GM with fun, trivial info, which is a good thing.
If using your chart or table during play increases the experience of play simply by virtue of using it while you are playing then that is so good. Please, do that more, designers.
If the chart is more like procedural encounter or dungeon design or other things that computers do better than someone with dice and paper and pens, I can't think of the games in which that would be more work than it's worth (but I can totally think of at least one and it sounds awesome to me, in my head, when I tell me about it).
Dungeons are about exploring and interacting with facts. Sometimes possibilities work (like, say, what's in the Goblin's Pocket) because they're for describing parts of play that are about you and the player discovering things together. As a GM, I don't want to run the kind of dungeon we discover together, because of things like stakes, and fairness and me not being amazingly good. As a player, I really, really, don't want to explore a dungeon we discover together with the GM, for all those reasons and more.
Dungeons are dangerous or boring and hiding either of those things behind a die roll makes things a bit more complicated (forces the GM to stop and consider how to signal the presence of the danger) and/or more boring (adding rolls and lookups before something boring makes it more boring, adding it before something dangerous doesn't make it more exciting and probably less exciting because it lengthens the time between interactions).
I think you can probably make on-the-fly dungeons work by breaking the backbone of early D&D and making it about the characters and GM creating a place together by asking questions. I also think that you don't need a GM for that (no need for someone to mediate/referee between the game and the players )and I also think there are games that work like that, on the macro level (Microscope) and a plenty of games like that that work on the micro level - they just so happen to be video games. Or, at least, I can't figure out how to make it work or why I'd want to keep trying (but prove me wrong! I want to be wrong!)
*which is more fun, anyway. Also, I probably didn't take these lessons to heart for a while.
** And, even then, only if you've determined ahead of time that they must be there. B/X and OD&D suggests one or two dungeons to start (I think). You might have other maps that you'd like to use, but they don't exist until you need them. Or maybe they do. I tend to think they don't because I find that makes for a much better game, but that's me.
***I suspect that one of the reasons there are so many active blogs about older D&D is because of the need in older D&D for making table and charts and these kinds of details and the sort of joy and creativity involved in making them and the fact that they are awesome and the only people you know that isn't another GM with a blogger account who thinks they are awesome are the players – the one group to whom you probably can't and shouldn't show the tables.
****I also think there is an important performance element to consider: take Zak's example of a good slow table (rolling to hit, rolling damage – these are systems designed to draw out and make more exciting a process that happens in much less time in real life); what you're performing by rolling through a nested table at play that's meant to be run through all at once like, say, “what is in this room?” is that you don't know what's in the room. Which can be fine, but it can also be, and usually is, not fine.