In Action Tale, Magic is a major theme, but as the stories go we can see there are various ways to interpret what magic is, and how it's done properly. At the Wormbar, not all central characters are able to perform it, but most characters wish to be able to use it. We can see another level into this question, at the Action Tale blog. Magic is a secret, held secret to keep those secrets in the right hands.
In parallel with magic, we can see monks have powers, and there's a number of other possibilities, as psychic, things called manifesting, fae tricks, etc. There's a very limited number of monsters in this universe, but those are most of the time called powers, no magic. The first Epic Destiny campaign, Stolen Dreams, do show at the Wormbar that some people's magic is stronger than other one's, and also there are three types of Magic, being Arcana the older, Divine only with proper weekly rituals to a God/dess, and Natural also called New Magic, but most users need to make a weekly ritual named Attune Ritual of Arcana, to enter attune state with Magic itself. A new Goddess of Magic insist in that the power must be the owner's, not from a godlike entity.
It looks like there's more to come, and this Story haven't shown all about Magic.
In the setting of Mu, there's no definition if what the Moai do is magic or not, if it's a way of power, or even if the elementalist abilities are other.
The label "Other" is attributed to anything characters don't know exactly what it is, but the effects will be most of the time similar to one between Magic, Manifesting or Power.
One important characteristic of magic abilities is that you can master a spell, and so it will work even under specific contrary situations. This mean you can use it in areas of Dead Magic (Magic Faul) and also in areas of Savage Magic, but powers are mostly linked to some type of trigger ability to recover from use, most of the time it's a natural condition, such as heat/cold weather, meditation, or some time of rest. Manifesting is different, and the manifester don't usually chose what happens, when manifesting.
There are three basic Magic users: Wizard/Witch (natural user, with inborn ability), Sorcerer (a manifester), and Mage (a schoolar user, be dinastic, academic or arcane family user).
Many others exist, as Alchemist, Elementalist, etc.
There's also a lesser type of Magic, which is called Stonecasting. It's most used everywhere, as this may be used by common people, as soon as they learn to activate the stones, which are special stones in which an arcanist imbue a specific Spell to that stone, which is said then to be "charged". Some empires do a large effort into the collecting of these stones to be used by it's population. Price depends on the Spell charged, and availability on the market, from 1-2 golden pieces, til 50-250 golden pieces. Spells of type Utility are the most important, and so one will find them easily, in most stonecasting empires.
Also, Magic is explained in a huge number of different theories, so to the level of an individual understanding of those theories, with it's applications changing in the individual level, but most Magic Laws are universal, with major exceptions being dangerous and harmful magic being called Dark Magic.
The major paradigm of Magic includes the oposites, represented by Dragons, with positive arcana magic, djines in the middle, with neutral wishmaking magic, and Sectoids on the final, with Snakelang language being called a black magic language, spoken by giant Naga oracles and Basylisks, negative magic. One character says in a passage of Stolen Dreams: "Everyone uses black magic, but they don't scream around the corner they do", so people just don't need to know that, and mostly this is a silent secret. So well, this is something you will find during your studies of the subject, but beware.
The Dark Magic is said to affect Lucidity, the ability of understanding and to express oneself.
Then, let's hope your magiker doesn't simply get mad.