Exclusively Light magic users, The Enclave is viewed by many as a paramilitary organization, enforcing their views of Magic on the rest of the world. In reality, it has many facets: while there is a focus on combat among a segment of their members, they view themselves as a sovereign organization, with their own police force. They also have researchers and historians.
The Enclave is a completely self sufficient (and in their minds, autonomous) organization, spread across the globe. They have secured treaties in most countries to allow their operations, and they at least make a show of cooperation.
While the Enclave allows for general membership by any magic user who passes their test, as well as non-combat roles, such has historian or researchers, or students, they prefer to find magic users as young as possible and raise them from children.
At the top of the Enclave is the Council. Council Members are often treated as heads of state, and they are the be-all-end-all of decisions made by the Enclave. It is rare for them to be seen in public.
Guardians are the backbone of the Enclave's military strength, to the extent they admit to having one. Guardians are trained to deal with illegal magic usage. They are part police officer, part peacekeeper, part magical consultant. Their job is, in theory, to protect other for magical abuses and be the eyes and ears of the Enclave.
Knights are the offensive arm of the Enclave. Knights are exclusively promoted from the ranks of the Guardians, and often are assigned the same duties. However, Knights have also been trained in more offensive usages of their abilites are are considered the most elite of the Enclave's fighting force.
Every Elemental Magic user (whether or not they know it) is a member of 'The Council of Mages'. Generally shortened to 'The Council', it is ruled by the most well-known Elemental Magic users of their particular element, known as 'The Circle'. Appointment to The Circle is handled by a vote of the existing members, the most influential of which is voted in as 'The High Mage'. It's no secret that The Circle is an entirely political body; Circle members often like to flaunt their status.
Because of how openly political they are, many people like to characterize The Council as a country club, or other social clique. The key difference, however, is that The Council vehemently fights for the rights of Elemental Magic users (and often magic users in general). The members of The Circle keep their position by keeping their respective constituents happy; a Fire Mage Circle member who, say, doesn't speak out about a ban on Fire Mages on public ice-rinks will suddenly find a younger, more charismatic Fire Mage has taken his seat in The Circle.
Because The Council aims at being all inclusive, most Elemental Magic users identify themselves as 'Mages'. The phrase has entered common parlance, and is now an accepted term for someone who isn't a member of the Enclave, or clearly a dark magic user.
Split into regional Covens, The Association claims its goals are promoting a better understand of magic, and furthering the interests of all magic users. This is undermined, however, by the fact that they only admit Dark Magic users, and really are nothing more than a special interest group. They have championed the legalization of Dark Magic for decades.
Recently, they succeeded in getting a law passed in the United States that all Dark Magic users above a P3 must register as a member. Those who cannot meet the financial requirement may apply for financial aid. Dues are tax deductible.
These are magic users of all kinds who pursue Magic in a scholarly fashion. They tend to avoid political entanglement, however, all other magic groups recognize their value and importance. The G.H.A.W. rarely accepts new members, and when they do, those individuals are expected to spend the rest of their lives studying and learning about magic.
It is because of their singular focus that the G.H.A.W. is one of the only groups to produce new spells. They will accept commissions, but they choose their client very carefully. Small modifications often only take months; some commissions take years. There are even rumors that some spells have been in development for decades, with the client passing ownership (and payment duties) on to their children.
Like a majority of cults, this one sprang up around a very charismatic and powerful leader. Unlike most cults, this leader is a P12A. Hekate (her real name is Heather Collins) has modeled herself after the greek goddess and modern goddess of Wicca. She claims to be the actual embodiment of the Goddess, and therefore she is above the laws of this world. Her followers aren't simply being duped; the woman has impossible to believe powers, and is one of the most powerful Dark Magic figures in the public eye.
The Church has been in legal trouble for the last decade; they have applied for and failed to receive official recognition as a religion. Due to Hekate's particular blend of charisma and power, however, the Church is very powerful, filled with very successful individuals. Their legal team has been having a string of victories, and it is only a matter of time.