Where there are laws of magic, it is almost inevitable that, sooner or later, someone of an academic persuasion will try to quantify them and that, sooner or later, they will be studied, either in their own right or as part of a formal education in magic. Such study is traditionally referred to as thaumatology1 and is a logical part of any world in which magic behaves predictably. Depending on the setting this may be hidden, occult lore or part of the school and university curriculum - and may be subject to (pseudo)scientific investigation or learned by rote and developed by guesswork and accident.
Thaumatologists are the people mostly likely to create an in-universe system of schools of magic (even if there is no mechanical basis for them) and to develop complicated grading systems for spells and their users. Where there are a variety of sources of magic, all may be studied or one or more might be ruled out of scope for a variety of reasons (e.g. theurgy for relying mainly on the whims of super-sapient entities rather than on cosmic laws2) or shamanism for being little more than high powered haggling). That said, they may well be able to tell the various practices apart and, for example, tell witchcraft from more acceptable forms of magic and perhaps even identify a particular magical tradition in the same sort of way that hoplologists can tell various martial arts from one another.
A thaumatologist need not necessarily be a practising magician (although it probably helps), and a thorough understanding of the subject may or may not have any bearing on your magical abilities (although logically, it should also help).
Where magic is inherently wild or chaotic, or otherwise not prone to universal rules, thaumatology is more likely to be either a fools errand or a branch of anthropology.
Game and Story Use
- As noted, significance will depend on setting.
- All other things being equal, this is a good skill for the more academic, smart-ass sort of magic user (assuming that there is any other kind), for NPC sages (especially those called upon to identify unusual magic items and effects) and for the professors of a "wizard-university".