a magic system
Combining 5th edition Dungeons & Dragons' schools of magic, some older editions' ideas about divinity, and my obsession with organisation, I've produced this. May it serve you well!
Categorisation
Magic is broadly organised by what processes it has undergone. A 'spell' is still technically formed of the same arcane energy as any other spell, but the way it's expressed is what determines what 'kind' of magic it is.
"Arcane" vs. "divine"
These are the two broadest categories of magic. Arcane magic comes directly from the stars, is bounced off a caster, and expressed directly. Wizards are arcane casters, and magic produced from magic items is arcane as well. It has, at most, been stored or channeled through an object. It hasn't been meaningfully altered by the media it's passed through. Divine magic comes 'from' something. For example, a warlock granted their powers by a devil is always casting divine magic, since the devil channels the magic directly to them. Importantly, the caster is a valid candidate for an intervener when deciding if magic is arcane or divine. A sorcerer whose soul is a font of draconic magic is still casting divine magic, in technical terms. A druid, casting spells by pulling energy from the nature around them, is casting divine magic.
Divine subdivisions
Divine magic is further divided into internal and external magic; the former being magic brought forth from oneself, and the latter being magic granted by a deity1. Psionics (focused energy of the mind), metamagic (alteration of arcane magic through force of will), spiritualism (empathy given form, channeled through nature), and ki (energy of the physical body) are examples of internal divine magic.
External magic is divided into the true and false categories. True external magic is granted by an 'actual' deity, while false external magic is granted from any lesser immortal.
Arcane subdivisions
Arcane magic is divided into 'invented' forms, called dunamancy, and 'natural' forms, called pure arcane magic. These are divided into 'schools' (though divine magic is often categorised into the same schools based on its effects).
Schools of dunamancy include graviturgy (manipulation of gravity), chronomancy (time), hydromancy (the sea), and bladesong (a certain elvish technique). The pure schools are abjuration (protective), conjuration (transporting), divination (revealing), enchantment (affecting the mind and body), evocation (manifesting effects), illusion (deceiving), and necromancy (manipulating life).