I keep seeing people chat about the various kinds of rules you can use for magic systems in tabletop or video games. While I don't mind this kind of conversation, it always strikes me as a bit weird, kind of like asking "I wrote 'the'. What word can come next?"
To me, the rules in a game should support the theme of the game. I don't mean anything particularly deep or precise, but just in general. For example, the Dark Sun setting has a very different feel than Mass Effect. They are completely different, and their themes are different. Dark Sun is about a world collapsing under the weight of environmental apocalypse, while Mass Effect is about heroically fighting to make the universe a better place even if those in power are not interested in helping you.
Well, I'm sure most people would phrase it differently, and both settings have had enough re-interpretations and changing writers to wander away from whatever the original theme might have been. But the basic idea is that the themes of these worlds define a lot about how their rules work, and how their rules work determines a lot about how their in-world societies work.
I think most people who create worlds just want to create something of their own, and that's fine. But when I see them aping the clumsy D&D recipe, it makes me uncomfortable. D&D is fractured and incoherent from most perspectives, largely due to the number of iterations. For example, with the rules they use for magic, societies cannot be structured the way they are. Magicians and clerics would dominate. Later on they tried to fix this by making warriors into mages (but calling their spells things like 'feats'). This doesn't help. It may help combat balance, but it makes the world make even less sense, and doesn't change the fact that mages and clerics, with their excessive noncombat utility, would still dominate society.
When you make this kind of argument, most people handwave it. "You're thinking too much, it's just got to be fun."
But that's the thing that annoys me. Having a theme does not make things unfun, it makes things resonate better, stick in your head better. That's why people like Warhammer 40k despite it not being significantly better or worse than the hundreds of other miniatures games: it has an extremely clear theme. To the point where we non-fans make fun of it. The fun-ness of a game is unrelated to how well themed it is - no reason not to have both. Have a game which is fun to play but also resonates well.
The most powerful tools to create theme are mechanics and setting. Those are the two things that the players touch most often. Obviously a heavy authorial touch will make them feel preachy or one-note, but there's no reason to leave them completely generic.
So, when I see a question asking for a list of all the different kinds of magic systems, my first instinct is to say "what theme?"
Are you trying to create a grungy steampunk setting, full of industrial oppression? Then your magic system should either support the rise of industrial steam (golem/device magic) or it should have been supplanted by that rise (some kind of slow nature magic). Whether it involves spellbooks or limited casts per day or some kind of material or whatever - those are specifics that fall into place pretty quickly when you know what role the magic plays in your world.
One problem is that magic, in particular, tends to dominate these kinds of settings. It's rarely a good idea to separate your classes into "this one can warp the fundamental stuff of the universe and this one can't". IE, the classic "mage/fighter" divide. That's a lazy default that doesn't really make any sense. Every iteration of every fantasy game since the original D&D has struggled to boost the nonmagic classes and nerf the magicians, because fundamentally "magic" is more powerful.
I recommend just accepting that. You can have a wide variety of classes that use or fail to use magic in many different ways. Once you start to invent your mechanics, the class options start to unfold.
For example, if you decide your steampunk game is going to include both a device style magic and a much older nature magic, you can start to lay down classes. First, there's obviously the oldschool nature magician, someone who can call upon life and storm. They are weakened when they can't - being inside is generally bad for them.
On the other end of the spectrum are the steam warriors and engineers. The warriors carry around the big devices - steam drills and pressure cannons and pneumatic armor. The engineers are masters of their craft, which is more like metalbending than anything directly related to steam, so maybe they carry around miniaturized devices that use high-power springs and coils rather than actual steam. It's much lighter... but also has less power.
Since it's basically metalbending, we could have a classic mage of that variety to match our classic nature mage. This would be a blademaster who uses metalbending not to create devices, but to create superhumanly sharp swords and a screen of flying knives. Also, good at picking the huge metal locks people use, so I guess this is our rogue.
As you can see, the classes kind of fall into place. We could continue to create more and more unusual classes if we wanted. For example, a class which has plant fibers woven through their flesh using a variant on the nature magic. However, it's often good to keep the classes pretty obvious, because otherwise you need to do a lot of exposition and explaining about how things work. It's better for it to just be intuitive, at least initially. All these basic, intuitive classes are likely to be the ones that the NPCs are, so therefore they are also powerful social forces that shape the society.
What I mean is that you can build the framework of your industrial oppression on these four basic classes. The nature mages are being oppressed, both by the encroaching industrial cities and systematically by the industry that hates how they get in the way. The engineers are dominant, creating the factories and machines that the industrial cities require. Warriors - and, more generally, users of any kind of steam technology - are the meat of the setting, the middle class. Oldschool metalbenders would come off as obsolete, maybe a religious group or something. You can build your world from these blocks, and it all works out because we kept our eye on the the theme from beginning to end. So even though we didn't create the classes with the society in mind, since both the society and the classes descend from the theme, they still work together.
So... um... that's it, I guess.