epic poem vs rhapsody

epic poem and rhapsody both are nouns.

Word	Noun	Adjective	Verb	Adverb
epic poem	Yes	No	No	No
rhapsody	Yes	No	No	No

As nouns, rhapsody is a hyponym of epic poem; that is, rhapsody is a word with a more specific, narrower meaning than epic poem:

Other hyponyms of epic poem include chanson de geste, heroic, heroic meter, heroic verse.

epic poem (noun)	rhapsody (noun)
a long narrative poem telling of a hero's deeds	(in ancient Greece) an epic poem adapted for recitation
	(music) a free instrumental composition in one extended movement; typically emotional or exuberant in character
	an enthusiastic expression of emotion