paean vs hymn

paean and hymn both are nouns.

Word	Noun	Adjective	Verb	Adverb
paean	Yes	No	No	No
hymn	Yes	No	Yes	No

As nouns, hymn is a hypernym of paean; that is, hymn is a word with a broader meaning than paean:

paean: (ancient Greece) a hymn of praise (especially one sung in ancient Greece to invoke or thank a deity)
hymn: a song of praise (to God or to a saint or to a nation)

Other hypernyms of paean include anthem.

paean (noun)	hymn (noun)
a formal expression of praise	a song of praise (to God or to a saint or to a nation)
(ancient Greece) a hymn of praise (especially one sung in ancient Greece to invoke or thank a deity)

paean (verb)	hymn (verb)
	praise by singing a hymn
	sing a hymn