When you are talking about genres, it is mainly a matter of perspective. For example: We typically refer to games that have complicated character stats and experince systems as a Role Playing Game (RPG). However, in almost every game you play you are playing the role of somebody. Therefore, Call of Duty 4 is a Role Playing Game. So is Grand Theft Auto. In Quake III, I decide that going up high is not wise as it is more likely I will be killed. I can now call Quake III a strategy game.

We therefore categorize games into genres to describe what the game is like. FPS implies that the focus on the game is running around and shooting things. Games like these tend to be more action oriented and multiplayer based such as Quake III. FPS has a large emphasis on the shooting part. FPA (First Person Adventure) implies that the focus of the game is having an adventure. Couldn't really find a better way to describe this, maybe: completing a set of objectives that span a large, open world where there are many logical and environmental obsticals to overcome (even if it is linear, as long as it feels you are physically going from one spot to another). FPA tends to be single player based.

HL2 and Corruption are vary different. Just like how there are a bunch of different RPG and RTS games. But, according to my views outlined above, both HL2 and Corruption fits the FPA mold better than FPS.

This is making me feel old!

FPS meant single player, first person perspective with a gun - i.e Doom, Half Life, etc.  Its only more recently (from my aged point of view) that FPS has become so linked to MP (not that coop and MP weren't there from the start on PC).  In fact I think an earlier comment implied FPS meant online MP only with FPA = offline SP.  Funnily enough for me FPS still means SP with MP as a great add-on to have fun with your friends with when you're not focused on the SP campaign.

DOOM:

1) There is no open world.  You go from one level to the next.  The overworld map is just a picture to make you feel that you are going from one area to the next.

2) There are no logical or environmental obsticals to overcome.  Just colored doors.

3) The emphasis on the game is in shooting aliens, nothing else.

4) Repetitive gameplay that is better geared towards multiplayer.

Now you may be talking about DOOM3.  In that case, change #1 to open world.

HL2:

1) The world is open, even if you have to travel in linearly.

2) Many puzzles to overcome.

3) The emphasis is on completing the objective.

4) More varied environment for single player.

HL2 is more of an FPA than DOOM.  I don't know if I am describing it very well.  Just look how boring and repetitive DOOM3 is on single player.  That is because they tried to take FPS rules and turn it into a single player game.  It ends up being one room after another of "walk in and shoot stuff".  HL2 varies it up much more and turns it into more of an adventure (<--key word).

Like I said before, FPS and FPA are loosly defined.  I don't see why you would insist HL2 is not an FPA since it is the emphasis on adventure that made it a great single player game.

I'm pretty sure DOOM couldn't have had better puzzles other than find the key and figure out how to get to that one platform, given the technology. So for it's time it too was an FPA. Same with quake, there was a lot of jumping puzzles. Also it wasn't on shooting aliens, it was to press the EXIT button or switch, and figuring out how to get to the keys that enable you to do so.

And no, HL2 world was NOT open. Also I the tech actually allowed something other than jumping to be considered a puzzle. Removing the ridiculous advancement in tech, DOOM and HL2 are basically the same. DOOM3 was very adventurous in itself, atmosphere it set up was amazing and traversing the dead halls of the UAC base was definitely a special feeling. Zelda is an adventure, Metroid is an adventure, HL is not.

according to Webster, an adventure is

1 a: an undertaking usually involving danger and unknown risks

therefore, HL2 is an adventure.