song vs carol

song and carol both are nouns.

Word	Noun	Adjective	Verb	Adverb
song	Yes	No	No	No
carol	Yes	No	Yes	No

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

Other hyponyms of song include cradlesong, lullaby.

song (noun)	carol (noun)
the act of singing	a joyful song (usually celebrating the birth of Christ)
a short musical composition with words	joyful religious song celebrating the birth of Christ
the characteristic sound produced by a bird
a distinctive or characteristic sound
a very small sum

song (verb)	carol (verb)
	sing carols