Most primitive religions have only shamans --- or witch-doctors or demipriests or whatever one wishes to call them. One good technical term is "hop"; it covers all religious functionaries that (a) perpetuate a cult they did not start, and (b) are not a part of a larger ecclesiastical hierarchy.
More evolved religions then have a real hierarchy, which usually starts with priests whose function is to keep order over other priests: the generic name for such a job is "bishop".
Religions of the ultimate frontier, then, do away with the whole ecclesiastical class, and treat every member of the religion as a priest: not as lay priests, but as real priests with all the exorcistical, demonological, theological and blessingitional powers that would otherwise given to hops, bishops, Popes or even the gods themselves. The technical term for such a singular priest in "trishop".
I hope this clarifies some things. Also, there is no such thing as a "quadrihop"; that would be just silly.