hymn vs paean

hymn and paean both are nouns.

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

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

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

Other hyponyms of hymn include dithyramb, doxology, choral, chorale, canticle, hymeneal, pean, recessional.

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

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