I'll stick my toe in... (long essay warning)
Let's start with the easy one:
Megadungeon - as far as I can tell, the one defining feature of a megadungeon (as opposed to just a really big dungeon or series) is that it is open-ended at the design level. Need more rooms? Just tack 'em on. Party going where the map is blank? Start drawing! The archetype here is Castle Greyhawk. Undermountain is close; they've already done much of the tacking on for you but the suggestion is still given that you can expand as required, and you still have to populate and flesh out about 99.9% of the rooms and areas on the maps.
The next size down might be called a "campaign dungeon", but there's some sub-types here as well. The defining feature of these could be that while there is assumed to be a world outside or beyond the dungeon, there is little reason given to interact with it - if desired, the campaign need never leave the confines of the dungeon.
Campaign, Stand-Alone - this is just a single ordinary closed-design dungeon that has failed a save vs. Enlarge. Rappan Athuk is a good example: you can spend an entire campaign just bashing around in that one dungeon, every now and then going to town for gear and training. Temple of Elemental Evil is another. World's Largest Dungeon could be another but I don't know enough about it to say if it's a Stand-Alone or a Path (see below).
Campaign, Exploratory - a single somewhat-closed area with the possibility of lots of little sub-adventures that is in fact one great big dungeon in and of itself that can, if desired, represent a whole campaign. Myth Drannor is one such. Ravenloft could be seen as another.
Campaign, Adventure Path - a closely-linked series of adventures that in fact are really just one great big adventure broken into bite-size chapters. These are designed such that the campaign starts with the first adventure in the path and ends with the last one. Amount of interaction with the off-path world is up to the whims of the players and-or DM. War of the Burning Sky is one such.
There's another level to insert here, where a series of adventures form a linked path but do not make up the entire campaign:
Series, Adventure Path - same as Campaign, Adventure Path but rather than being itself the entire campaign it is instead contained within a larger campaign where other adventures may occur before and-or after the one path. Rod of Seven Parts and the G-D-Q series are two examples. (note that while the G-D-Q series can easily be the endpoint of a campaign it will never be the start point, unless the campaign starts at considerably higher than 1st level).
And then there's the more conventional module-style dungeon or adventure The big difference here is that interaction with the outside world beyond the dungeon is both assumed and expected before, after, and sometimes during the adventure itself. Further, the campaign by definition is going to consist of at least two of these modules and usually many more.
"Lair" is a bad overall term for these as it forces assumptions about what the adventure or dungeon consists of; so I'm going to use "Module" instead. There are, of course, many sub-types:
Module, Lair - adventure consists of invading the lair of a nasty critter or a BBEG and killing the occupants. Mission complete when occupants dead. Keep on the Shadowfell is one such, of many.
Module, Recovery - adventure consists of finding and recovering something e.g. a person, item, knowledge, whatever. Mission complete when target recovered and returned to safety.
Module, Exploratory - where the party have to explore an area or find their way to-from somewhere, includes modules where the focus is a journey rather than the destination (e.g. Journey To the Rock), also includes modules where the party is lost or disoriented (A4 Slavers Dungeon is in part one such; Q1 Demonweb Pits is another). Critters and opposition are a secondary focus. Mission complete when journey/exploration complete.
A sub-sub-type here would be Module, Pursuit - adventure consists of pursuing someone or something but not catching it. Usually a sub-adventure in a path of some sort, but can occasionally work as stand-alone as part of a campaign where the mission is complete when the party turn the chase over to someone else.
Module, Mini-Path - where the adventure consists of several smaller quasi-linked chapters but is not in itself big enough to wrap a campaign around. Often includes elements of all other module types. Night's Dark Terror is one such.
At the module level, the definitions of course become blurrier - many modules incorporate elements of different types, with the one over-riding feature being that after finishing the module they're in the party goes on to something else that may or may not be related at all. Forge of Fury is an interesting example: it starts out as a Lair, becomes Exploratory during play, ends up returning to Lair at the end, and depending on why the party is there at all could also be classed as Recovery.
Thoughts?
Lan-"I admire your patience if you read all this"-efan