In its simplest form, magic is the use of Vimana through a Catalyst for the sake of bringing out a predetermined end called a Spell. The average magician knows only a handful of spells, and those that know more tend to know various varieties on the same spell.
 
Modern Equestrian magic is divided into six schools of magic, which divides all known spells into subcategories for ease of study. They are
 
Ignem, coming from the Latin word for Fire, refers to the elemental manifestations such as the creation of fire, lightning, ice, earth, as well as weather manipulation and other manipulation of forces.
 
Aurum, coming from the Latin word for Air, refers to all spells that move an object through space, including telekinesis, teleportation, time travel, as well as spells that grant flight or burrowing.
 
Aquam, coming from the Latin word for Water, refers to any and all spells that transform one object into another object, such as shapeshifting, polymorphing, as well as most forms of Alchemy and potion-making. Aquam also covers spells that create objects ex-nihilo.
 
Terram, coming from the Latin word for Earth, refers to any and all spells used primarily for defense, shielding, or warding.
 
Corpus, coming from the Latin word for Body, refers to all spells that manipulate the bodies and souls of living things without transforming them into something radically different. It thus covers all the healing arts, as well as necromancy.
 
Mentem, coming from the Latin word for Mind, refers to all spells that manipulate the minds of sentient beings, as well as those that enhance the perceptions of the caster.
 
This system was devised by Mage Meadowbrook around the year 230 NE, based on the Unicornian School of magical practice. It is not absolute or complete, being a method of categorizing spells, not an actual description of different kinds of magic. Below is a short list of where all spells in FEMTO could, theoretically, be placed. Note that differing fluff could easily result in a new classification, and although treated as the same spell here, fluffwise a dozen different fluff "spells" could be made out of a single mechanical ability.
 
Ignem: Wrath, Slow, Elementalist, Magic Bolt, Homing Magic, Storm Bolt, Haste, Orbital Strike, Night, Earthen Strike, Climate Control, Empower Weapon, Arcane Arms, Spell Resonance.
 
Aurum: Telekinesis, Teleport, Armed Ally, Astral Projection, Dreamwalking [not a mechanical skill, but a fluff one]
 
Aquam: Shapeshift, Nature Elemental, Hat Magic, Doppelganger, Animal Totem, Ethereal Weapon, Unholy Elementalist, Conjure Weapon
 
Terram: Bolster, Inure, Protective Bubble, Spell Breaker, Retaliate
 
Corpus: Heal, Mend, Healing Bonds, Prayer of Healing, Commune, Raise Dead, Lifestream, Control, Corpse Explosion, Bloodborn, Enfeeble, Resurrect, Abomination, Return to Earth, Magic Boon, Healing Hammer, Don't Die on Me, Tartarian Power, Polymorph, Grave Strike, Necromachines
 
Mentem: Mind Reader, Transfix, Animal Mastery, Animal Swarm, Moment of Peace, World Warp, Fourth Eye
 
A Note on Necromancy:
-Despite necromancy and healing spells being part of the same school of magic, Corpus, there is absolutely no reason Aether would know about necromantic practices. The only knowledge she likely shares with the average necromancer is knowedge of equine anatomy, but the magic necessary to repair a body is NOT the same magic necessary to inflict unlife on a dead body.
-Necromancy in Equestrian society is taboo, but not illegal, and while many necromancers are available who might know Commune and be willing to conduct seances [for instance], such things are not commonly engaged in. The average Equestrian wouldn't dream of visiting a creepy sorcerer and ask to speak to a lost loved one. Also, while raising the dead to serve as servitors is not illegal, graverobbing still is, making legal acquisition of corpses a difficulty for the non-academic necromancer.  
-The spell Resurrect, as well as the skill Reincarnation, should not be treated as common knowledge. If there are immortals walking around, or mages who can raise the dead in truth, they are not known of, and their arts are buried in lost libraries or under lock and key in the Canterlot Archives.
 
Misc Notes:
-Despite being extremely associated with ghosts, the Astral Plane is not particularly associated with Necromancy in Equestria due to the simple fact that the association between ghosts and the plane is not known, given the extreme rarity of ghosts in Equestria. It is more commonly associated with wizards using it to spy, or spirits that can enter it at will such as Windegoes.
-Other forms of power, such as Psychic Powers and Supernatural Abilities, are known of in Equestria but are not as academically studied or vastly comprehended as Magic. In other parts of the world they are given more deligent study [see Chineigh and Japone's interest in Supernatural Abilities], but in Equestria it is common [but erroneous] to simply lump all these abilities together as 'magic'.
-Intellectually, Aether would be well aware that most forms of Anima are not in fact 'magic' by a technical definition, since it does not involve a Catalyst, just as she would be aware that the energy powering Earth Ponies' strength or a dragon's breath are not technically 'magic', but the error is along the same lines as calling a spider a 'bug', and even a scholar may not ruthlessly cling to exacting terminology all the time.
 
Schools by Class:
Ignem: Mage or Cleric
Aurum: Mage
Aquam: Mage or Shaman
Terram: Cleric or Paladin
Corpus: Cleric or Necromancer
Mentem: Cleric, Necromancer, or Shaman