Why don't you just say "randomly generated"?

That is literally what the term means. It just makes you sound stuck-up or like you'd found a thesaurus and want to use more expensive-sounding words to seem clever.

I don't know who's "you" in your post, but technically speaking, as the word is used on GOG in some games' descriptions, it's rather procedurally than randomly generated. Randomly you can deal the cards or allocate character points. If you generate levels or quests, it's random-based but still some complicated procedure – because you need to assure to make those random-based choices consistent and logical.

I suspect it was to try to drive home the fact that the randomization in any decent "proc gen" game tends to be pretty heavily structured (as opposed to "true" randomization, which would create unplayable garbage a large proportion of the time). I think the term procedural generation might've already been in use in some slightly different fashion in programming/software fields, so it was probably just a case of someone glomming onto the term and (mis)using it as something of a marketing term (yes, possibly in part to sound impressive, whether consciously or not).

Personally, I would prefer "procedurally randomized", as it conveys that rule-based aspect of the current popular sense a bit more clearly without stepping on any other (probably earlier) meaning, but "randomly generated" is O.K., too, in the "most people probably get what you mean" way. It's probably a moot point, though, as "procedurally generated" is a pretty entrenched term at this point (much like the use of "roguelike" to describe any "run-based" game making heavy use of randomization).

No, it doesn't.

For example: Random level generation would mostly produce broken levels with inaccessible rooms or items, impossible geometry, etc.. A run in a truly randomly generated universe in No Man's Sky would be over on the first planet because more likely than not the next planet would be too far away to even be reached or the starting planet would have no resources or it would be an unsurvivable death world or a thousand other things. Procedural generation on the other hand uses complex sets of rules to make sure that the outcome while not predetermined is still logical, coherent and actually functional in the game context.

No, it doesn't.

It simply means that the game world/levels/whatever were not made by a human but were generated by the computer through an algorithm. That algorithm might include some form of randomization (and nowadays often does) but doesn't have to.

Actually, the very first game which used procedural generation (Elite from 1984) didn't use randomization at all, as far as I know.

Counter-example: The worlds of Arena and Daggerfall are (mostly) procedurally generated, but are the same every time you play. (Excluding things like Arena random quest dungeons and the radiant quests found in these games, which are, actually, random.) Rogue (1980) says hi, and the Wikipedia article claims it wasn't the first game with procedural generation.

As other said, it doesn't mean that it's totally random. There are still some specific rules that the algorithm needs to obey to ensure that player can proceed further.

Otherwise without rules, the algorithm could do things like stick key for chests inside the chest they unlock and keys for doors inside the rooms they unlock. Procedurally genrated would not allow the computer algorithm to do either.

Also in computing, there's no such thing as Random. Due to the logical and strictly binary nature, most "random" things are instead "seeded", that is the computer will look at a rapidly scrolling list of numbers and pick what happens based on that specific number it saw.

Seed 52959=You rolled a 7.

Which drives us to the very core philosophical questions about deep nature of the world! :D
I recommend "The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics" of Roger Penrose, however the lecture might be a bit tiring (:

Procedurally

Adverb

1. (manner) According to a procedure; following a procedure.
2. (manner) In a manner that is concerned with procedure.

Synonyms
(concerned with procedure): methodically, systematically

Procedural (comparative more procedural, superlative most procedural)

Adjective

1. Related to procedure.
2. (computing) Generated by means of a procedure, rather than being designed.

Literally

Adverb

1. word for word; not figuratively; not as an idiom or metaphor
Synonyms: actually, really, unfiguratively, unmetaphorically
Antonyms: figuratively, metaphorically, virtually

2. (degree, figuratively, proscribed, contranym) Used non-literally as an intensifier for figurative statements: virtually, so to speak (often considered incorrect; see usage notes)
Synonym: virtually

3. (colloquial) Used to intensify or dramatize non-figurative statements.
4. (colloquial) Used as a generic downtoner: just, merely.
Synonyms: merely;

Because I thought it was called "procedurally generated" bacause that's the term I've seen used before. No thought or ulterior motive behind it at all :D

A bit of correction. Firstly - a succinct definition is that the data is created by a computer / algorithm rather than manaually. and you are right, this can be done by either a random seed or a fixed seed.

The correction - Elite is not the first game that used procedural generation, as almost all games have been using some levels of procedural generation before then (and almost all games today does, just to save space). But you have games like Beneath Apple Manor from 1978,which came out 6 years before Elite, and used it a lot.

Anyway, the game I used to examplify procedural generation is Frontier: Elite 2. which is fixed and not random (in other words, every time you play you have the same galaxy). Frontier containes over 200,000,000,000 stars (most with orbiting planets and moons) and about 30,000 inhabited planet. It has space stations, a large variety of ships, a physics engine, seamless surface-to-space transitions and the actual gameplay. The closests stars to our sun are correct. On the Amiga this came on one singe floppy disk, and even then the disk was not full. If you look at some sites where you can downloaded it today, it is ~457 KB. The only reason why they managed to cram a whole galaxy into this size, is that the galaxy is procedurally generated.

This is also how it is used todya. take Skyrim - do you think that for example every single trree and leaf are made by hand? no, they are procedurally generated from a fixed template, just imagine the file size Skyrim would have needed if they where manually generated.

edit - and the same goes for modding. when you have a mod that changes the apperance of threes in Skyrim, do you think that the modder is sitting there and remoddeling eveyr single leaf in the game?

You are right, Rogue is older than Elite and uses procedural generation as well.

It's strange though that Elite is listed in pretty much all literature as the first game using it. It is even listed in the Guiness Book of Records. Maybe they only count commercially released games and Rogue wasn't commercially released until later.

Or maybe Guinness is an utterly garbage book?