Arcane magic focuses on pure imagatination and the fundmnetal energy of manifestation. There is pure arcane magic and then elemental magic that is arcane being modified into manifesting as an elemental property such as fire. The two different locations to learn arcane magic teach a different collection of spells. A.E.G.I.S. focuses on a basic arcane magic but has watered it down so that it will manifest various elements. The Arcane Sanctum has a few elemental spells but for the most part they are focused on the most powerful manifestaion: pure arcane.