I was actually planning on asking something similar. Basically it seems that magic in the Warcraft universe is heavily based on magic from D&D (and why not? It's basically the father of RPGs).

In Dalaran you can read books on the schools of magic. These schools are the same ones that appear in D&D (abjuration, conjuration, divination, enchantment, illusion, necromancy and transmutation), with one important omission. The school of evocation. In D&D this is the school into which all direct damage spells fall, such as fireball, cone of cold, acid splash, etc. These schools do not simply pertain to arcane magic, but also the divine spellcasting of druids and clerics. In WoW terms:

• Abjuration is shielding magic, like mana shield, but also power word: shield
• Conjuration is summoning magic, like conjuring food and water, elementals, and demons
• Divination is scrying magic, and magic that can see the future, like the shamanic farseers and Med'ivh
• Enchantment is like magical sleep effects, weapon enchantments, and mind control
• Illusion is things like mirror image
• Necromancy is anything that deals with death magic, like the Lich King's powers
• Transmutation is turning one thing into something else, like polymorph or druidic shapeshifting.

Lore-wise, the mages that you play in the game are evokers (even if that school was omitted in game), because that's the way the game is set up - you are a damage dealer. Realistically though there would be mages that specialise in one specific school to an absurd degree. Illusionists, Abjurers, Conjurers, Enchanters, while still knowing spells from other schools. The whole frost/fire/arcane thing is just a style of play, but they are all mostly evocation spells.

Most spells in the D&D universe have a vocal component, but I'm not sure about whether there is a specific language of magic. I'm even less sure about the WoW universe.

Additionally, arcane magic in WoW is done by manipulating the energies of the universe directly. In druidism, shamanism and the powers of the light, magic is channelled through an intermediary (spirits of nature, the elements and the light respectively), which is why they are not addictive and considered 'safe'. The caster is asking this intermediary to do what they ask, but arcane magics are a result of you manipulating the energies of the universe directly, and it causes a drug like rush, commanding all that power yourself. You want to do it again, and again, and again, until you can't live without it. Anyone who's smart enough can learn how to use arcane magic, but it takes practice. There are some though who are born with an innate magical ability.