church music vs music genre

church music and music genre both are nouns.

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

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

church music: genre of music composed for performance as part of religious ceremonies
music genre: an expressive style of music

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

church music (noun)	music genre (noun)
genre of music composed for performance as part of religious ceremonies	an expressive style of music