A bit of both really. The kind of mage you are depends upon which source you draw from. Pyromancers are practitioners of something called 'wild magic' (or 'esmer'). Pyromancers are very distant from their roots as practitioners of wild magic and consider themselves separate from the likes of other esmer magi. However, their power is natural. They are able to draw from the sun, or any local source of flame, but when they can't they can draw from themselves ('inner fire'). And yes, this is something exclusive to pyromancers, and is somehow (won't give it a way) linked to the extinct dragons and the dragonsouls (also known as 'phoenixes' in this world).

In saying that, it is somewhat grounded. The strength of your power is determined by your strength as a living being. Younger, more vivacious magi are a lot more powerful than older magi, and their bodies can take a lot more punishment (as magic is very much a part of your being). This being said, there are many older magi that can still wipe the floor with their younger counterparts.