flamen vs non-Christian priest

flamen and non-Christian priest both are nouns.

Word	Noun	Adjective	Verb	Adverb
flamen	Yes	No	No	No
non-Christian priest	Yes	No	No	No

As nouns, non-Christian priest is a hypernym of flamen; that is, non-Christian priest is a word with a broader meaning than flamen:

flamen: a priest who served a particular deity in ancient Rome
non-Christian priest: a person who performs religious duties and ceremonies in a non-Christian religion

Other hypernyms of flamen include priest.

flamen (noun)	non-Christian priest (noun)
a priest who served a particular deity in ancient Rome	a person who performs religious duties and ceremonies in a non-Christian religion