I'm still having trouble understanding the distinction. Does this mean that as long as the players can decide between exploring the haunted mansion, the goblin caves and the old ruin, all three remain situations, but once the players decide to go for one of the options, or if the DM only presents one option, that option becomes an adventure? But then, how does this gel with the following point:
Does this mean that in order to present his players with situations instead of adventures, a DM should not do any preparation at all? If not, So how does preparation for a situation differ from preparation for an adventure?
Firelance: the difference between an adventure based design and a situation based design, is about the nature of the preparation the DM does. In situation-based design, player choice is king. In adventure based design, story/plot is king. I will illustrate below but be aware that the examples I am choosing are extreme because I am trying to show you what I mean: in reality NO game is totally one or the other.
An adventure is fairly scripted and is often about story. You have a dungeon/site map, a load of encounters and a preset assumption about how the Players will react to the site, often in the form of a hook. So in a adventure, the DM has defined, the "site", the "obstacles" and the "goal" ahead of time and he also chooses the time when the adventure takes place in the campaign arc. The players then choose how to tackle the adventure, and "right" and "wrong" are usually more black and white, to simplify the process of getting the PCs into the game. in addition, the background of the campaign world is often only an afterthought, and is window dressing. There is also often a connection between one adventure and another that is a kind of plot, story-arc or theme. This is what published module for 3/4E tend to be like.
A situation based game, often called a sandbox, is different. You can run one with almost no prep, as long as you know the rules and the rules lend themselves to this style of play (e.g. 1E was good but 3E was bad for sandbox/situation type games) but you have to be very good at improvisation. However, I usually prepare, even for a situation based game, except that my prep is completely different to adventure prep.
If I want to run a situation-based campaign, then I will create a campaign area that has many cities, many wonderous locations and many NPCs, though often only in broad brush strokes. They will all have their own flavours and agendas and motivations.
I will have quite a detailed campaign map, together with maps of major settlements and major important locations, though certainly not all major sites.
There will be lots of background material: cultural and linguist traditions, a well worked out chronology of feast-days and other events that will occur in the year as well as a complex idea about things like religious, regional and national attitudes. Bascially, I will build in alot of potential for conflict.
I might also work out some events (political, magical, disasters, wars etc) that will occur throughout a campaign year ahead of time, though these events will react to certain player/PC actions. There will be no over-arching logic to any of this: the situations really are just things that are happening.
I would also grab every map, picture and encounter from published adventures, web-sites etc that I can lay my hands on and organise them so that I can find them at a moments notice when DMing. There are a number of web-based random wilderness and dungeon generators if necessary.
I will then let the PCs investigate and explore. They will make allies with whom they wish and fight who they want. They will go where they want, when they want and I will have to keep up.
Often what happens is that the PCs will decide to visit a certain (undetailed) location and I will throw in some encounters on the way, to promote roleplaying, to keep vermisilitude etc. There encounters will be in keeping with the nature of the areas they pass through and will be dictated by wandering monster tables that DO NOT SCALE with level. These encounters also perform another valuable function: they stall the players. As sessions last 3-4 hours, a few encounters is enough to ensure that I then have prep time between sessions to fill in the gaps. Or else, they would arrive and penetrate a tiny way in (often winged) and then the session would end and give me time to prepare.
Now you can see why it is best to run a game that includes elements of both design philosphies as neither works well for an extended period.
To answer your first question though, if the three dungeons are all mapped out, and one must be visited out of the three, and the players "relationship" to the dungeon is scripted/assumed, then all three are adventures.