Never played Magic the Gathering; in MoM Blue is school of enchantment.  It has spells like Spell Blast, Fly, Time Stop.  Wanting to add to op and not detract from your idea.

  I think I would do something with Runes, Sigils, Glyphs.  Each one could be made up of 1 or more schools of magic.  Schools of magic(pretty much all the old standards from rpg's/books). 

  Runes could be be placed on armors and shields, swords and other melee weapons. 

  Sigils could be used to enhance cities and army battle standards(which could benefit the troops).  Standards, streamers and assortment of other flags on a pole.  Maybe something like a glaive.

  Glyphs could be used as battlefield or open map trap, trick, or disguise.  Units and/or map features like mountains, hills, forests as well as buildings could be effected.

What about magic by culture instead? You seem to be touching on this with your chinese and japanese examples.

Conjuration (Scientific manipulation of the world)  - Alchemy, Elemental Destruction, Summoning, Enchantment, etc.

Divination (Using Deity Worship) - Revelation, Divining, Spying, Troop Communication, etc.

Wizardry (Historical Knowledge of Spells) - Teleportation, Displacement, Portal Summoning, Elemental Manipulation, Levitation, etc.

Voodoo (Ancestral Worship) - Possession, Elemental Manipulation, Divining, Enchantment, etc.

Each of these would be different philological ways of using magic that is based on using the magic stored in shards (each containing one of five different mystical elements) and a school's specific rituals and pools of knowledge to affect the world.

This way emphasis is on the cultural understanding of magic and potentially incorporate all culture's unique use of the term.