Wiccan magic — both as practiced in the "real" world and as depicted in Buffy The Vampire Slayer and, to a lesser extent, Charmed — is mostly Theurgy. When Magic itself is a kind of entity with which casters make bargains and cut deals, this becomes a variety of Wild Magic.
Broadly if your magical practice and your religion are one and the same - or even if they overlap significantly as in Kabbalah then it's probably safe to call it theurgy. Shamanism is another popular form of theurgy (although not nearly as popular today as it seems to have been in the past).
In some RPGs this school includes Summon Magic, in which the caster summons the entity itself to wherever he is and bosses it around. As one might imagine, this can easily lead to the entity turning on its would-be temporary master if done wrong, especially if the entity is a demon or some other form of Always Chaotic Evil. See also Deal With The Devil. This is a somewhat poor fit with the rest of theurgy as one does not generally summon ones deity and bark orders - even shamen, who traditionally deal with entities a long way down the scale of things that get worshipped will normally use more courtesy in their dealings.
Respectful summoning, as might be undertaken by a theurge (possibly summoning one of his deity's minions) might be termed Invocation.
Theurgy describes the practice of rituals, sometimes seen as magical in nature, performed with the intention of invoking the action or presence of one or more gods, especially with the goal of uniting with the divine, achieving henosis, and perfecting oneself.
Game and Story Use
- Theurgy blurs the line between religion and occult, and the line between magic and divinity. There's some serious potential for heavy gaming in those gray areas.
- It also opens the possibility of magic itself being an NPC (or, PC if you're really brave and innovative). A powerful PC witch might have to coax power and favors out of a tempermental NPC spirit. Said spirit may also require an Equivalent Exchange, so Be Careful What You Wish For.
- The summon/invoke dichotomy can be useful if you leave it in place - where a theurge invokes respectfully, a summoner is rude and disrespectful … possibly getting faster and more reliable results in the short term, but having far bigger problems when things go wrong.