big business vs business sector

big business and business sector both are nouns.

Word	Noun	Adjective	Verb	Adverb
big business	Yes	No	No	No
business sector	Yes	No	No	No

As nouns, business sector is a hypernym of big business; that is, business sector is a word with a broader meaning than big business:

big business: commercial enterprises organized and financed on a scale large enough to influence social and political policies
business sector: business concerns collectively

Other hypernyms of big business include business.

big business (noun)	business sector (noun)
commercial enterprises organized and financed on a scale large enough to influence social and political policies	business concerns collectively