dance band vs big band

dance band and big band both are nouns.

Word	Noun	Adjective	Verb	Adverb
dance band	Yes	No	No	No
big band	Yes	No	No	No

As nouns, big band is a hyponym of dance band; that is, big band is a word with a more specific, narrower meaning than dance band:

dance band: a group of musicians playing popular music for dancing
big band: a large dance or jazz band usually featuring improvised solos by lead musicians

Other hyponyms of dance band include combo, jazz band, jazz group, rock band, rock group, steel band.

dance band (noun)	big band (noun)
a group of musicians playing popular music for dancing	a large dance or jazz band usually featuring improvised solos by lead musicians