pax vs greeting

pax and greeting both are nouns.

Word	Noun	Adjective	Verb	Adverb
pax	Yes	No	No	No
greeting	Yes	No	No	No

As nouns, greeting is a hypernym of pax; that is, greeting is a word with a broader meaning than pax:

pax: (Roman Catholic Church) a greeting signifying Christian love for those assisting at the Eucharist
greeting: (usually plural) an acknowledgment or expression of good will (especially on meeting)

Other hypernyms of pax include salutation.

pax (noun)	greeting (noun)
(Roman Catholic Church) a greeting signifying Christian love for those assisting at the Eucharist	(usually plural) an acknowledgment or expression of good will (especially on meeting)