Welcome.
I think that you might have it difficult with categories of Magic, there are more ways to break it into categories:
Community difference
Chaos magic(individual system that person develops themselves basing on their own creativity, experience and resources)
traditional magic (systems shared among more people, for short or even very long time)
Locality of foundation of the system
European, Middle-east, America, Africa, Asia, or closer... Japan, China, Iceland, Hawai, etc...
History:
Ancient reconstructed
Middle-age
Modern
cyber-age
Hands
LHP - Left Hand Path
RHP - Right Hand Path
More ways of sorting:
Religion, colors, reputation, sources and resources needed...
