This is starting to come together. Finally.
What is Theurgy?
In general terms, theurgy is the practice of interacting with spirits in order to achieve a supernatural effect. A priest petitioning God to heal a wounded soldier is practicing theurgy; so is a necromancer securing a ghost to a corpse, or a shaman asking a fire-spirit to light his cigar. Where it differs from magery is that spirits have their own opinions and agendas; some can be overcome, but others much be placated or persuaded. On the bright side, theurgy is typically quieter than secular magic. Actual evidence of actual, true, and fully Divine Interventions (or Infernal Interventions, either) is rare.
In game terms, ‘theurgy’ is what happens when a magic user has Invoker instead of Mage. Mages can make magic items; Invokers can ward against and even banish evil influences. It roughly evens out. There is nothing particularly stopping a priest from also being a mage, or vice versa: but Invoker and Mage pools cannot be combined.
Types of Theurgy
Clericism is the interaction of men with gods, or at least demigods. It is simultaneously the most powerful and most capricious form of theurgy, as it regularly entreats with supernatural entities that are more powerful than the theurgist. And gods are notorious for having expectations about their priests’ behaviors.
Shamanism involves spirits of lesser power; ‘natural’ ones are the most common, but there are other types. A powerful shaman can bind and command, but a wise one placates and entreats. A spirit in a bad mood can be extremely dangerous, bound or not.
Necromancy deals with spirits of the dead. Depending on who one asks, this is either low-grade demonology or something else. The Imperium Orci’s Christian priests are expected to only interact with spirits via exorcism (either gentle or otherwise); Second Republic Christian ministers have been known to bind human ghosts into human corpses for ethical purposes. Speaking with the dead is usually considered safe enough, particularly if the goal is to get the spirit to move on to the afterlife.
Demonology is, as the name says, about working with demons. It is not taught by any reputable, ethical magical school; and the Dominion doesn’t teach it, either. Somehow, though, there always seems to be a grimoire or two around that can provide the necessary instructions.