inscription vs epigraph

inscription and epigraph both are nouns.

Word	Noun	Adjective	Verb	Adverb
inscription	Yes	No	No	No
epigraph	Yes	No	No	No

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

inscription: letters inscribed (especially words engraved or carved) on something
epigraph: an engraved inscription

Other hyponyms of inscription include superscription, epitaph.

inscription (noun)	epigraph (noun)
the activity of inscribing (especially carving or engraving) letters or words	an engraved inscription
letters inscribed (especially words engraved or carved) on something	a quotation at the beginning of some piece of writing
a short message (as in a book or musical work or on a photograph) dedicating it to someone or something