Primary difference between these and human magic classes: these make no use of demons (anti-Light entities) or the Light. (Light as mentioned in elemental magic is light, not Light; sunlight, moonlight, starlight, firelight, but not the Light.)
Notes: Various races will call each class a different name, so I'm going to just term them generically. Also, I'm not going to include warrior-magic crosses, as they should be self-explanatory; warrior-mages keep their proficiency with weaponry and physical combat, as well as all but the most difficult/refined magical skills of their particular class.
Pure Magic Classes
weather magic, the extended elements (water, fire, air, earth, metal, stone, crystal, as well as shadow and light)
plant magic (growth, cultivation, enhanced herbalism, alchemical herbalism, gardening/farming, wood magic), animal magic (behavioral aspects, senses, partial and/or full shapeshifting, herding/domestication, companionship/protection)
communion and interaction with gods/spirits/ancestors/living/dead, shared sensory input or full control of spirits/ancestors/living/dead, psyche magic/manipulation, sound/music magic
arcane ('raw') magic, power storage/management, sensing/perception of magic use, manipulation of inanimate objects, use and charging of tools/objects, formal or ceremonial rituals/spells
healing, cursing/hexing, buffing/debuffing, disease/plague, purify/cure, pain/exhaustion, peace/revival
Note: Manipulation magic is the physical side of speaking magic, which affects the personality/psyche, whereas manipulation affects the body/living spirit. Yes, the spirit is felt to be physical, far moreso than the mind.
Crossover Magic Classes
World Magic (elemental + living)
weather magic, elemental magic, plant magic, animal magic
Change Magic (speaking + manipulation)
psyche magic, communion and/or control of various entities/people, healing/hexing, buffing/debuffing, plague/cure