song vs piece of music

song and piece of music both are nouns.

Word	Noun	Adjective	Verb	Adverb
song	Yes	No	No	No
piece of music	Yes	No	No	No

As nouns, piece of music is a hypernym of song; that is, piece of music is a word with a broader meaning than song:

Other hypernyms of song include composition, musical composition, opus, piece.

song (noun)	piece of music (noun)
the act of singing	a musical work that has been created
a short musical composition with words
the characteristic sound produced by a bird
a distinctive or characteristic sound
a very small sum