classical music vs music genre

classical music and music genre both are nouns.

Word	Noun	Adjective	Verb	Adverb
classical music	Yes	No	No	No
music genre	Yes	No	No	No

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

classical music: traditional genre of music conforming to an established form and appealing to critical interest and developed musical taste
music genre: an expressive style of music

Other hypernyms of classical music include musical genre, musical style.

classical music (noun)	music genre (noun)
traditional genre of music conforming to an established form and appealing to critical interest and developed musical taste	an expressive style of music