jazz group vs jazz band

jazz group and jazz band both are nouns.

Word	Noun	Adjective	Verb	Adverb
jazz group	Yes	No	No	No
jazz band	Yes	No	No	No

As nouns, jazz group and jazz band are synonyms defined as:

Other synonyms of jazz group include combo.

jazz group (noun)	jazz band (noun)
a small band of jazz musicians	a small band of jazz musicians