For my Jewel of the Desert (Dungeon World) game:
There are four main traditions of magic in the Tarrakhuna, the region where the game is set. Those are the Waziri Order (wizards), the Safiqi Priesthood (clerics and paladins), the Kahina (druids and shaman), and the Rawuna (bards.) There are underlying common elements for them, but also ways in which they are totally distinct.
Waziri magic is fundamentally analytical and imitative. It can be extremely dangerous to cast Waziri-type magic without a proven arcane formula first (as in, "blow up a whole building" dangerous), so Waziri mages tend to be very conservative with their spellcasting. (In theory this could be abused, but the whole "you will definitely die and probably kill all your friends too if you do this" angle helps reduce that issue.) They look down on other disciplines because most forms of magic they can imitate or recompile into Waziri format, which is it's greatest strength, but they are incredibly jealous of their work and thus advancement overall can be very slow. Hence, the reason everyone uses the same Fireball spell is that that's a formula which escaped the jealous clutches of its creator and which provides provable, consistent results. It's sort of like learning new chemical reactions; once the secret gets out, people will copy that reaction rather than trying ti reinvent things themselves every time. New spells can totally be developed! But that sort of thing either happens very slowly or only arises from being able to analyze (usually destructively) magical effects created by other disciplines. Few Waziri can heal, but it is possible for them to learn (it's just very difficult, as anatomy is difficult to account for in mathematical formulae.)
Safiqi magic is the magic of faith, exemplars, and banishment/judgment. The priesthood studies theology and the lives of saints in order to understand the divine and how mortals have called upon its power. The Safiqi (lay and clergy) worship the One, a being they claim is the infinite and ineffable creator of all that exists. The One, they claim, cannot be understood in Their entirety but must instead be understood through Their infinite aspects or facets that are individually finite and digestible. The "prime" aspect is the Great Architect, the facet understood as regarding creating, preserving, planning, and ruling; other known facets include the Unknown Knower (knowledge, stealth, research, concealment), the Stalwart Soldier (reactive protection, loyalty, hardiness, play/sport, solidarity), the Resolute Seeker (hunting, purification, revelation, proactive protection), and the Soothing Flame (light, healing, fire, community, kindness.) Most Safiqi spellcasters dedicate themselves to some specific facet of the One, which shapes the manner of how they do magical things, but not the specific spells they have access to. The Safiqi can do a lot, but they are completely incapable of calming the spirits of the unquiet dead; they can rebuke or temporarily banish them, but cannot resolve the problem, only the next group can. Because they all share one common religious origin, their spells are all the same.
Kahina can be split into two groups: druids and shaman. The former, also known as Kahina of the "living" spirits, interface with spiritual/primal energies as they manifest in the world itself, moreso than in the spirit world. Hence, they learn to take the power of "living" animal spirits into themselves (shape shift) and work with active, concrete manifestations of natural energy like elementals. Shaman, or Kahina of the "dead" spirits, tend to be more in tune with the subtle background of spirit activity; they see the spirit of a forest that slowly coalesces from the spirits of many trees living in the same space for a long time, that sort of thing. They also contact the more distant, "archetypal" spirits that permanently reside in the spirit world. Instead of bringing these spirits into themselves, they bind spirits to totems and call upon those totemic spirits for aid. Unlike the Safiqi, all Kahina can lay the unquiet dead to rest (druids pull dead spirits back into the current flow of life energy; shaman send dead spirits on to their final rest in the spirit world.) However, Kahina cannot banish otherworldly spirits from the world, at least not powerful ones like devils and demons. Most Kahina practice magic in a way that doesn't involve "spells," but those who do are tapping a common wellspring (the knowledge of the ancestors as obtained from the spirit world and transcendental spirit journeys), so the few who do cast spells proper do so in similar ways.
Finally the Rawuna, the bards who paint the sky with their tales, are the most eclectic and hard to pin down. Which is quite fitting, really. Most Rawuna get started with basic Waziri education before learning from the Nomad Tribes' oral historians. Rawuna can learn from almost anyone, sort of like Waziri, but do so in a poetic, humanities-focused kind of way rather than the STEM-style formulae if the Waziri. The way this has manifested in game was a player (effectively) breaking down and rebuilding the story of the life of a particular Safiqi saint, not as a theological study, but as a tale to grip the soul and fill the mind with beautiful images (allowing the party Bard, after sufficient effort, to cleanse poisons and toxins with his Arcane Art, in addition to the standard effects.) Rawuna thus don't really have "spells" in the usual rigid sense, but just as four-chord songs are super common, you can find common themes (pun intended) in Rawuna practice.
The only other major form of magic is a dark reflection of Safiqi magic, practiced by a breakaway heretical sect, the Zil al-Ghurab or (as we more commonly say it) the "Raven-Shadows." They're a fanatically devoted assassin-cult who practice shadow magic, which is related to Safiqi magic but much more aggressive and generally less supportive. This isn't a form of magic most people even know exists, though, so it's much less well understood than the others. It has some connection to devils, however, and retains the Safiqi emphasis on banishing influences which do not belong in the world (and the inability to get rid of restless dead who are, properly speaking, native to the world and thus not outside influences to be banished.)
The players themselves, across two games, helped to define what the magic system was of this world. I mostly just played a guiding/coordinating role, with the ideas largely coming from the players. We haven't explored the depths of Rawuna magic much, despite having a Bard, but that appears to be changing. We'll see what further revelations await!