priest vs flamen

priest and flamen both are nouns.

Word	Noun	Adjective	Verb	Adverb
priest	Yes	No	No	No
flamen	Yes	No	No	No

As nouns, flamen is a hyponym of priest; that is, flamen is a word with a more specific, narrower meaning than priest:

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

Other hyponyms of priest include Druid, hoodoo, lama, magus, priest-doctor, shaman, votary.

priest (noun)	flamen (noun)
a clergyman in Christian churches who has the authority to perform or administer various religious rites; one of the Holy Orders	a priest who served a particular deity in ancient Rome
a person who performs religious duties and ceremonies in a non-Christian religion