Here's some snippets from how I define it on my world of Orea.
I'll be updating the thread,
http://www.enworld.org/forum/plots-places/284160-orea-world-its-people.html with more specifics on the magic of that world later today if anyone wants to check it.
But specifically for "Arcane" magic here's what I have:
"Magic on the world of Orea is a form of all pervading energy that is able to be harnessed and controlled to various effect in any number of ways. The sources of magic on Orea are classified by the sages of Flin into:
Arcane -the magic of wizards gained through study, practice and research,
Divine -the magic of priests and paladins gained through meditation, prayer and the divine favor of their respective deity, and
Natural (also called "Primal") -the magic of the druids and other classes and creatures (like shamans, the Sorarynae, and the natural abilities of the zepharim) gained through ancient teaching/practices, innate ability and/or communion with the ambient energies of the cosmos."
and...
"
[SIZE=+1]Arcane Magic[/SIZE], also call Arcanum, is the magic of study. The magic of wizards and sorcerers. The energy of Arcane magic flows through the whole of the realm, like air. It is self-perpetuating and replenishing, the energy is "built in" to the world of Orea itself. These energies are capable of being harnessed through spells and rituals."
To illustrate the distinction, this excerpt from the section on Natural Magic.
"[SIZE=+1]Natural (or Cosmic or Universal or Primal) Magic[/SIZE] is the primordial power of the world of Orea itself. The residual energies of the entities Ahl and Zho (who created the world and heavens and then departed them and their creations (dragons and titans). If arcane magic is an energy that flows throughout Orea like air, and divine magic is bits of essence of the gods, then Natural or Cosmic magic is more like a radiation that emanates from, with and through everything, everyone, everywhere. "
--Steel Dragons