Stigmas are a physical manifestation of a psychic or occultist's difference from humanity. As stated in the Second Edition rules, a stigma does not necessarily have to be connected to the use of an occultist's powers, but often it metaphorically tied to them. A Sixth Sense psychic might have an eye twitch when using his powers, or a telepath might whisper uncontrollably when connecting with a target's mind. They can also be obviously occult physical deformations- elongated canines, strange birthmarks, or even hairy palms. The close knit communities of the Known Worlds often identify individuals with such deformations early, and due to the prevalence of superstitious beliefs that those marked with these strange signs are cursed many psychic children are cast out or handed over to the Church.
Theurgic stigmas are a bit different. Like psychic stigmas they are a physicalization of the occult difference between the theurge and the community. Theurgic stigmas, however, often manifest in ways which inspire awe in the faithful: some theurges suffer the appearance of lash marks on the arms and legs in the same places the Prophet was beaten by Disaporan nobles, others have their clothing stained red with blood in mimicry of the wounds of St. Mantius. Whether it is speaking in tongues or sleepwalking (attributed to St. Paulus), theurgic occult stigma appear closely connected with the Prophet, and the vast collection of Church saints that followed after him.
As a rule, then, psychic stigmas are typically those things which identify them as occult in a fashion that marks them as strange, whereas theurges (who typically manifest their stigmas when their theurgic power is gifted to them) often have more clearly religiously themed stigmas.