Origin is probably an important part, too. Naeve and Nithya are from a separate plane, it seems, so it would follow that demons may come from elsewhere as well.
As far as my own character goes, Aria's particular species is very Earth-bound. The official title is Material Demon; they're like an embodiment of greed. Each has control over a worldly luxury: precious metals, jewels, nice cars, furniture, foods, books, electronics--anything somebody has coveted has a Material Demon attached. Some abilities are broader than others, some may overlap, but that's the general idea. As I said, this makes them incredibly worldly: without the world, they would not be.