Superman vs. Gandalf

Some years ago, I was reading a Shannara book (not something I'm likely to repeat), and one of the things that bothered me about it was how characters kept talking about "your magic" or "his magic is [x]." This language was grating because it contradicted my view of magic (formed from most fantasy fiction) as a singular force or tool that might be used in different ways, but was always just "magic." This language reminded more of a superhero setting. This got me thinking about what difference was between these approaches in terms of how fantastic abilities are portrayed.

It seems to me that there's probably a continuum with two poles:

Skill/Expertise: Fantastic abilities are accessed by training or learning, though as with any skill, some people will have a greater aptitude for it than others. The ability pretty much does the same thing for everybody, the difference is in the creativity of application and power level. Examples: Green lantern power rings, magic in the Conan stories or in The Dying Earth.

Unique Power: Fantastic abilities come in the form of idiosyncratic powers or at least one in a large array of powers. The focus is more on what a character can do rather than how good they are at doing it. Examples: standard superheroes.

Note that the names don't necessarily carry any connotations beyond the stated ones. For instance, the fantastic ability could be completely inborn or intrinsic but still fall into the "skill/expertise" category.

There is a category between those two that shows a greater variety of presentation. I would call this one:

Interesting Technique: Fantastic abilities have a common origin and common basic features, but individuals will develop a single unique application of sub-ability, or a small number of them. Examples: psi-powers in a lot of media, the powers of the Shimigami in the anime Bleach (fighting anime has this sort of thing a fair amount), the eponymous Exalted in the rpg.

The middle option tends to occur a lot when all the characters are of the same organization/origin, whereas the skill expertise approach is more commonly seen when fantastic powers are rare--but not always. There is a common variant where each power source/variety works like Skill/Expertise, but there are multiple power sources/varieties (bending in Avatar would be a good example). Also, settings can be mostly one presentation, but still have characters/groups show up that better fit another.