Styles of Prep - Games that Care
Yet another of the lies that Wizards of the Coast has sold TTRPG players, which they've bought into wholeheartedly, is that there are different styles of preparation, and all are valid for every game (because both are valid for D&D, and D&D is right for every game, of course.)
I'm gonna go over a couple games I've run, and explain that actually they all care about the type and level of preparation the GM does.
Indie games are often honest and open about what they want. To take a high-prep example, I recently ran Eureka: Investigative Urban Fantasy. It is not subtle! In the narrator section, right after the introduction, it says "We cannot advise you strongly enough to use prewritten adventure modules". It's not just there - throughout the rules, there's an emphasis that the situation, the state of the world at the outset and thus at every time that follows, is known and rigid. Eureka is a mystery game - the who, what, how, why, and more are all set in stone. The narrator is forbidden to change the scenario on the fly.
Eureka is very forceful of this because the authors, writing a game for mystery investigations, are well aware that it's damn near impossible to make a coherent mystery up on the fly. I'm sure they've tried. I've tried. It's impossible. Something will contradict, and you won't notice until well after the players have reasoned from that contradictory information. It can be done, but not well, and the mental load on the GM is going to kill them.
It's not a genre thing - Eureka is a game about the act of solving mysteries, but so in Brindlewood Bay. I don't have experience with Brindlewood Bay myself, but I do know that the GM doensn't have a real mystery ahead of time - there's a move which is rolled to determine whether a theory is correct. Both are mystery games, but they approach them differently - and each makes a vastly different demand of the GM's preparations.
On the opposite end of the spectrum from Eureka, more in line with Brindlewood Bay in fact, is just about every Powered by the Apocalypse game. Apocalypse World is very clear about what to prepare, and it's more or less the opposite of Eureka: "Daydream some apocalyptic imagery, but DO NOT commit yourself to any storyline or particular characters."
The rules actually tell you to start on what would typically be 'prep' during the first session: "Work on your threat map and essential threats". It's more like note-taking, at that point, just placing the names of stuff that gets mentioned in the session. After that first session, and between each other, you do some real out-of-session work, solidifying the notes you made into Threats.
I won't go into it at length, but Dungeon World is much the same - though there's no 'map' for threats, as characters are expected to be far more mobile, the system of solidifying problems that were mentioned in-game into problems with some mechanically attached descriptors is much the same.
Now, on to the elephant-sized dragon in the room - Dungeons and Dragons. The game itself is, truthfully, quite honest about this. It's the marketing team and the community, having fallen for their propaganda, who pretend low-prep is a valid way to play Dungeons and Dragons.
The 2014 DMG, correctly, focuses on prepared play. It asks DMs to consider "Do you like to plan thoroughly in advance, or do you prefer improvising on the spot?", but everything in that book is either rules text or preparation guides. Mostly the latter.
D&D, as it has existed since 3rd edition, (this is what I have experience with - I can't speak to earlier editions, except to note that there are alot of modules in their time and in the OSR tradition) is a game that thrives on prep. Even if that prep is procedural - tables of encounters and wandering monsters for an area, for example - it's impossible to run the game from nothing, without a lot of background, and have it work.
Imagine not knowing D&D, at all - you pick it up, read the non-list rules (so skipping most of the classes, races, spells, feats, backgrounds, weapons, etc) in the PHB and DMG, and try to run a game entirely improv from the rules and vibes. You'd quickly end up scouring the monster manual for appropriate encounters - and the game, by the rules, demands appropriate encounters! There's a budget system! It's a game about killing monsters and does a lot of math to try and make sure it's challenging without killing player characters.
D&D, at least in the books, is pretty honest about what it wants from preparation. It wants a lot! The playerbase pretends otherwise, but they're wrong. I've yet to find another game that tries to lie like this. Eureka wants you to use modules. Apocalypse World wants you to wing it. I have yet to find any game that actually doesn't care.