Theory of spells
Magical taxonomy is the classification of magic and, consequently, spells. Now I'm just going to give the general classification, without talking about the details in each area. I may dedicate more writing to each area after this.
As I said, not all spells are known; the possible number of spells is infinite. Think about the phylogenetic tree of life: all present extant species are just a speck of the number of possible ones. And an even tinier fraction is categorized. But this fraction is the most common, the most noticeable; and in magic the most useful and the most important. Here I'll describe the major known classes of magic with their associated aethers. Well, their associated families of aether, since not all aethers for one class of magic are the same. Under the name igneous aether, for example, we include all aether used to produce fire magic, but not every spell may use the same family of aether.
Each class or school of magic is casted with the aid of one class (type) of aether. The families of aether (subtypes), constituting together the class of aether, correspond to different families of spells. Even further down we get to genera of spells, which are spells with similar effects, related similar mind states and also use the same family of aether. For each genus of spells there's one generic spell, and we can consider other spells in the genus variations of it. If you master a generic spell, you can master its modifications. In fact, you almost never cast the same spell twice, there's always some minor variation because you almost never get the same exact mind state again.
The first ancient wizards may have either discovered basic magic or been taught it by some other species (maybe indirectly, through scrolls, inscriptions or runes). After that, the lore has been carried on for generations. Some people attempt to discover new spells, always related to major generic spells they know (again, it's all hierarchical: there are some spells within the same family closer to each other than others). If you go too far, most probably you'll do nothing. Another possibility is that the spell has an unknown effect, and it's hardly ever the desired one. When intelligent beings meet, they share their magic. Some races are very apt for magic; others aren't, even if they are intelligent. Some have more affinity for one classes of magic, other for others. The world is a very big place.
On to the classification. If you haven't noticed yet, I'm using Latin names for major concepts. Here I'll give the most common name and some other common names, and the best translation.
There are two major branches for all magic in the universe: amoral magic (magia amoralis) and moral magic (magia moralis). The difference is that while amoral magic doesn't employ voluntas (will), it's the basic requirement for moral magic. Almost all healing magic is moral magic; that is not the case for damage magic.
The pragmatical and most extended classification among humanoid sapient species attends to the physical nature of the magic. The two major branches are elemental magic (magia elementalis) and soul magic (magia animae or magia animica). You can also refer to soul magic as spiritual magic, astral magic or arcane magic lato sensu; the most unambiguous way to refer to it is as non-elemental magic.
The basic traits of elemental magic are the following: the aethers roam freely in the world, the physical effects are related to natural elements and it's generally amoral. It's the easiest magic to master, it can get really destructive, and it depends greatly on potestas "power" (voluntas rarely affects it, since it's generally amoral).
However, elemental magic is divided in two major groups itself: pure elemental magic (magia elementalis (pura)) or elemental magic stricto sensu and natural elemental magic (magia (elementalis) naturalis) or natural magic.
-Pure elemental magic is magic resulting from the materialization of two main classes of aether, which are opposed: igneous aether and aqueous aether. In other words, it contains fire magic and frost magic (magia ignea, ignis and magia aquosa, aqua). Frost magic is translated like that because most of the time spells have to do with frozen water, ice.
-Natural magic is magic resulting from the materialization of many types of aether, and two common clases are aereous aether and tellureous aether, which are opposed. It comprises wind magic (magia aerea, aeris), earth magic (magia tellurica, tellus) and more general natural magic. Among these types of natural magic we have magic which associates with living beings, such as plants; modifications of others (like storm magic for wind magic) and at some points this magic may become moral. This is so because, even if life and death are concepts not restricted to intelligent and moral creatures, they are usually accompanied by intent and will. We have the concepts of vita and mors here (life and death). Natural magic constitutes the only elemental school of magic which can heal, with the aid of vita.
Types of magic can mix. Some aethers have magical sign or magical charge. Fire is (+), frost is (-), earth is (+), wind is (-). Combos of the same sign can be very destructive physically; but combos of the opposite sign can have profound spiritual impacts (think of body as (+), soul as (-), and do the math). Some combos are really useful; others are rarely heard of. As usual, the details about aether behaviour escape us, we can only get some general trends. The sign thing explains why it's hard to master opposite forces, since you tend to get magically charged yourself. A fire mage gets "magically positive"; a frost mage gets "magically negative" (this may have side effects, think about libido or electromagnetic field forces).
As for wind and earth, the charge is not so marked because the spells are not so common (fire magic is a much wider area); they're usually mastered by druids or shamans who practise all type of elemental magic to a lesser extent. Some other pairs may exist within elemental magic, but the main ones are the mentioned ones.
The main trait of soul magic is that it's not based on any indepentently existent aether. However, this group is very heterogeneous, and it includes arcane magic, which is a really heterogeneous group itself. We can divide between moral and amoral magic:
-The amoral magic in this group is formed by arcane magic or arcanum. This groups constitutes magic itself. It includes most utility spells: transformations, enchantments, summonings, conjuring, shapeshifting, temporality, gravity, light, lore, etc. It can use practically any type of raw aether, be it whatever it is, which is why raw aether is sometimes called arcane aether. The real masters of arcane magic are mages, and are devoted to magical lore and knowledge. It's such a heterogeneous group that it's impossible to provide more general traits. It requires deep study and intelligence, and it can be very exhausting to delve into its secrets. Hence the name, arcanum, "secret". Arcane magic is amoral because its intent is knowledge of magic itself. However, some parts may be moral.
-The moral magic in this group is formed by light, white or holy magic (magia sacra, lux) and black or shadow magic (magia nigra, nox). Its main requirement is voluntas, and it affects the spell's outcome greatly. What matters is your intention: desire to harm, and you will; desire to heal, and you will. Most healing magic is holy magic. Beings with a fixed moral orientation are unable to cast the other: evil beings can't perform holy spells; good beings cannot cast shadow magic. It uses the same aether as arcane magic (raw one), but when it turns it into dynamic aether, the mind uses its moral conviction, which is why all what I said above holds true. It turns into luminous aether, light aether, for holy magic, or umbreous aether, shadowy aether, for shadow magic. Not to be confused with vita and mors: good and evil have been defined as order and chaos, not life and death.
Shadow magic is (-), holy magic is (+); because order is (+) and chaos is (-). Signs seem arbitrary but a lot of pairs in the universe have them (for example males (+) females (-)), the reasons are unknown.
As for damage, soul magic generally aims at the soul, the non-physical dimension of life (this a more relevant trend than the signs). Elemental magic tends to do a great deal of physical damage (again this trend is more relevant than the sign thing).