Tamer - summoners of lesser demons to do their bidding. Can be something as small as a Greenman (basically a little plant being) and something as horrible and large as a Niberius (basically a stitched together
Aira - Kind of spell casters without the spells. Demons all have Fatal Verses, lines that can be said to banish them back to Hell. Arias do nothing but memorize those lines and recite them. As far as I can tell
But yeah Doctor is pretty self explanatory, but they'll use traditional medicine along side more herbal remedies to deal with demonic wounds and illness
also you start out as a grunt and then move to a slightly more important grunt and then finally get certified but you're still pretty much a grunt for a couple more levels xD
and my own brain for wanting to exorcist au everythingspoilers=D;