program music vs piece of music

program music and piece of music both are nouns.

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

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

program music: musical compositions intended to evoke images or remind the listener of events
piece of music: a musical work that has been created

Other hypernyms of program music include composition, musical composition, opus, piece.

program music (noun)	piece of music (noun)
musical compositions intended to evoke images or remind the listener of events	a musical work that has been created