In my world, there are two types of magic: Runes and the Arcane Arts. There are specialties in each. Runes I haven't delved into too much since it isn't quite so relevant for The Colorless Dragons, but it is very common magic. The emberstone lanterns I keep mentioning are an example of Rune magic. Runes are carved into the lantern, imbuing the light with different hues or having the lanterns brighten as the suns set/dim as the suns rise. Rune magic is regularly practiced in certain professions (artificers being one of these).
The Arcane Arts are closer to actual magic as they involve the direct control of the Elements of Fire, Water, Air, and Earth without the use of inscriptions. Life and Death are also included, but they have extenuating circumstances. The Arts themselves are creation, manipulation, infliction, and communion. An Arcanist typically specializes in one or two Arts and one Element. For example, Braeik is a Water-infliction Arcanist, meaning that he can change his body's composition (or that of any other living thing) to water or ice. See Ch. 12 for a poorly described example.
On top of this, all magic uses Arcane energy, which comes from a Source (which constantly produces energy) or Reliquary (a temporary container for energy). Only some have the skill to manipulate Arcane energy and of those, few are tested and trained, which is why Arcanists are so rare.
I think you got me ranting, NJC... Hope that wasn't too much information. 
-Elisheva