Disclaimer: If true random exists in our reality, and what is the nature of free will are topics beyond this answer. The random I speak about in this answer is pseudo-random (when I say "random" take "pseudo-random" as implied). Also, for the purposes of this answer parameter vectors are also considered seeds.
I could not find an authoritative taxonomy of content generation. Thus this answer is the taxonomy of content generation as I - personally - make sense of it. I found an often quoted in literature "taxonomy of procedural content generation" in the paper "Procedural Content Generation in Games" by Shaker et al. published in 2016. I want to mention they use the terms deterministic and stochastic. However this answer remains my own take on it.
- Authored (designed) content: This is content generated by the authors of the game. Which might be bundled with the game, or be downloadable content.
Authored (designed) content: This is content generated by the authors of the game.
Authored content could use procedural generation tools which provides a result which is later refined by the author. This is known as offline procedural content generation.
Authored content might be bundled with the game, or be downloadable content.
- Procedural content: This is content generated by algorithms designed or selected by the authors of the game (there is a procedure that generates the content). The tools include pseudo-random number generators, generative grammars, noise functions, cellular automata, fractals, artificial neural networks and so on.
Procedural content: This is content generated by algorithms designed or selected by the authors of the game (there is a procedure that generates the content) during game play, also known as online procedural content generation.
The tools include pseudo-random number generators, generative grammars, noise functions, cellular automata, fractals, artificial neural networks and so on.
Procedural content generation can take different approaches:
- Constructive content generation: The algorithm produces content that is added directly to the output.
- Generate-and-test content generation: The algorithm has a loop where they produce content until it satisfies some fitness function. If it produces unsatisfactory content, it loops, until it produces satisfactory content.
- Search-based content generation: The algorithm searches a latent space of possible content that can be generated, using an heuristic, util it finds content that satisfies a fitness function. This is can be considered an special case of generate-and-test content generation.
The mentioned fitness functions could take the actions of the player into account.
- User-generated content: This is content provided by the players of the game.
User-generated content: This is content provided by the players of the game. This can also be classified as online and offline except this time we are talking about networking. The user-generated content confined to the game or the machine of the player is offline, and if it is shared over the network it is online. And then we can distinguish if the player receives user-generated content as part of normal gameplay, or they must request it.
- Predetermined※: It is always the same for everybody everywhere.
- Random (a.k.a pseudo-random or stochastic): It can be different every time. Using pseudo-random number generators, noise functions and similar tools.
※: What I call here Predetermined is often called Deterministic, however "predetermined" seems to be a better term because pseudo-random is deterministic (given the same input it produces the same output).
We will call content generation that takes the actions of the player into account as adaptive (and thus dynamic), otherwise we would say it is generic.
We could also classify the content generation based on whether or not the content generated is necessary to complete the game, or otherwise it is optional.
The designers could offer control over the seed values to the player explicitly (there is an UI where they input the seed) or implicitly (where the game derives the seeds from actions that the player performs, but the player is not told these action seed the content generation).
We can also collect fingerprinting data (e.g. user id, network id, hardware id, and so on), and hash it (we can also use HMAC or key derivation functions) to produce a seed value. In this case the content generation will be quasi-unique for the player (baring collisions). This allows us to provide content generation that is always the same for the same player, but different depending on the player.