There are four fundamental branches of magic. There are many sub-branches (mind magic, Artifact construction, etc), but these four are distinct from each other in the sense they behave differently and require entirely different knowledge to do well at. The first thing to note is all magic requires Intentionality. You need to be intending to (and be able to!) cast a spell before any magical construction will work, even if you do not activate the magic yourself. The second thing to note is all magic draws from the Primordial Ether, a sort of space or plane that mages can sense, and Spirits inhabit.
The first is the Prime Art, as it is called, of Sigils. The use of the word 'Sigils' is interchangeable with 'Spells' for the most part. In lore terms, Sigils have three major defining characteristics. Firstly, Sigils are Symbols. A drawn symbol in the air (or on paper, or on wood, etc). This symbol cares about Stroke Order and Direction. If you draw one of the lines up instead of down, whoops, no Sigil for you. Lastly, Sigils are Consumed. A Sigil cannot have magic flow through it time and time again. One the magic is put in, the Sigil ceases to be.
From the Quest's perspective, Sigils are your ordinary whiz-bang spells from every magical academy ever. Do a magic gesture, get a magic spell. You need to draw from your own Magic Pool to do so, but they can be cast quickly and effectively and are generally used for the most direct effects (cast shield, cast fireball, cast light, etc).
The second is the Noble Art, named so due to the propensity of the Undying to use Runes for nearly everything. Runes are your 'magical enchantment' school of spells. Put a Rune on something, charge it up, and it'll activate under the conditions you've set. 99.999% of magical gear is runic, (the remainder being Spiritual). Runes are Symbols, just like Sigils. However, Runes don't care about stroke order and direction. Instead, they care about Material. A Rune for Wood won't work on Steel, and vice versa. Lastly, Runes are Reusable. You can charge a rune again and again, and unless the physical form of the rune itself is compromised (your steel coin gets bent, your brick rune gets smashed), it'll keep on working indefinitely.
From the Quest's perspective, Runes are basically enchantments. Enchant an item to do X when Y happens is the general form of a rune. They're generally tougher to craft (depending on material), but are largely permanent (unless their activation destroys them, which isn't uncommon). They do require regular recharging, but they can be prepared well in advance of any combat. They're used for most magical infrastructure in society - the hot water in the showers is heated by runic pipes.
The third is the Art of Transference, named so because that's what Alchemy does. Alchemy is Magically Neutral, in the sense it doesn't care where the magic in it comes from. Runes and Sigils need magic from human Magic Pools. Alchemy can get magic from things Spirits have manifested as, human hair, plants in really magical areas... it's highly magically efficient. Secondly, Alchemy Transfers Attributes. You can make potions to transfer heightened awareness, the hearing of a cat, the strength of a bull, the stubbornness of a bureaucrat without the right forms, etc. Lastly, Alchemy is Not A Symbol. You make concoctions, you mix, cook, and stew. No drawing involved.
From the Quest's perspective, Alchemy is really just Potions. You put ingredients in, get magic drink out. It's main power is in buffing the player character, rather than direct effects. You can get potions to make you stay awake longer, heal faster, make you a lot stronger and faster, etc, etc. It's biggest disadvantage is that it's not really linked to the other two schools. Sigils and Runes are pretty similar, and a lot of skills can be used as effective cross-class skills (at half effectiveness) if you only have a Runic or Sigil-related skill. Alchemy has no such similarities.
The fourth is Spirits. Called the Saint's Domain by the Archipelago, and generally looked down upon by most mages from other schools. Spirit-Calling, Spirit-Talking, or whatever you want to call it is fundamentally unlike all the other schools of magic. Alchemy, Runes, and Sigils all require careful scientific thought, experimentation and testing to create better spells, runes, and concoctions. Spirits don't do that at all. Spirits are Functionally Random, you have no idea what a Spirit wants. What it will do generally depends on the nearby geography (Spirits that live near mountains generally like to be rocks or mountain-related things), but not always. Spirits are Hugely Variable. You can get a Spirit to form a rock. You might also be able to get that same Spirit to form an invincible rock golem to kill all your enemies if you figure out exactly what it wants and offer it that. Lastly, Spirits are Chatty. Being a cool guy who likes to talk to people is generally the best way to extract value from Spirits. Being an archmage of unparalleled power offers no real bonus.
From the Quest's perspective, Spiritual Magic is not like anything else. It's the "Wild Magic" equivalent - random shit can happen. Figuring out a Spirit completely can offer massive, massive bonuses (Spiritual Equipment can make the user the next best thing to actually invincible. Unlike Runes, Spirits can embody concepts, and if you managed to get a Spirit to wear who embodied the concept of 'Personal Defense', you might actually be immune to harm), but for the most part they don't. They also want weird shit, and will only help you actively while you help them. A Spirit might want you to make everyone wear badger masks, and doing it might turn said Spirit into a helpful badger who protected those it considered its young. However, it might protect everyone wearing a badger mask, which could backfire.
Mostly, though, Spirits can be asked to turn into physical shit (a rock, a tree, a body of water or ice), and this is the more reliable form of Spiritual Magic. The high-powered effects are rare and most mages will never encounter them.
