literary genre vs prose

literary genre and prose both are nouns.

Word	Noun	Adjective	Verb	Adverb
literary genre	Yes	No	No	No
prose	Yes	No	No	No

As nouns, prose is a hyponym of literary genre; that is, prose is a word with a more specific, narrower meaning than literary genre:

Other hyponyms of literary genre include drama, form, poesy, poetry, verse, satire, steampunk.

literary genre (noun)	prose (noun)
a style of expressing yourself in writing	ordinary writing as distinguished from verse
	matter of fact, commonplace, or dull expression