One division of magic that I like is from the Realms of Magic supplement for the original Marvel Super Heroes game. It splits magic into three types: Personal, universal, and dimensional.
For personal energy, think mental or chi powers. Telepathy, physical enhancement, and so on. They are easy and quick to cast, and just require concentration (no gestures or vocalizations). The downside is they use the caster's own energy, so they're physically draining, and when they affect others they require consent. You can't dive into an unwilling mind.
Universal is the energy of the surrounding universe, which the caster channels into various effects. This is the most like standard magic, and can include things like blasts, shields, teleportation, and illusions. It's also easy and quick to cast, and isn't personally draining, but does require the rituals of casting like gestures and words. Some of the effects can be resisted (saves i.e. Psyche FEATs).
Dimensional energies are tapping into beings or objects of power from other dimensions. This is the equivalent of "divine" magic, except based on weird fantasy instead of religions -- you're accessing the power of weird cosmic entities, demons, semi-sentient books, and so on. Dimensional spells are difficult to cast (typically a yellow instead of a green FEAT), relatively slow (end of round instead of during your turn), and require gestures and words, but no saves (Psyche FEATs) are allowed against their effects. The spells tend to be broad, powerful and/or do things other types of magic can't -- it's the only way to do certain things like dimensional travel or blocking or duplicating powers, and it can be easier to learn (dimensional teleport costs 1 slot while the universal version costs 2; and there are group spells where you can learn 5 related spells at the cost of learning a single dimensional spell).
The most unique type of dimensional spells are the entreaty spells, where the caster beseeches an entity. This is completely open-ended because you can ask for any effect (within your power rank), but the difficulty varies based on how suited the effect is to the entity's nature (the short list of things they're known for is easy, everything else is harder), and whether they're friendly to the caster/their school or not. There is a quid pro quo of some sort, but it's implicit rather than explicit -- most of the entities grant spells pretty freely, under something like the assumption that it spreads their power and glory across the dimensions. It's possible to entreat neutral or hostile entities, but they may draw the entity's attention, with the chance increasing as the caster becomes more powerful (think a powers check from Ravenloft).
There are also various traditions, which are a mix of philosophies and magical styles, including druidic, voodoo, faerie, schools associated with specific realms or pantheons, atlantean, scientific (alchemy), and more general ones like nature, chaos, and order (Dr. Strange is order, elder gods are a type of chaos). These schools often come with specialities (druidic is powerful earth magic, voodoo is powerful with the dead, etc.), and vulnerabilities (e.g. druid and faerie are vulnerable to iron). These are overlays on top of the energy types, and different entities may be friendly with certain schools and opposed to others.
It's a solid basic framework for looking at the different types of magic, if a bit underexploited in the Marvel Universe, which tends to mix them all together into mush. It wouldn't be hard to adapt it to gods, religions, pacts, psionicists, paladins, various schools of wizardry, monks, and so on. Could have more explicit and varied schools, entities of different ranks, investiture, and so on.