common carrier vs business

common carrier and business both are nouns.

Word	Noun	Adjective	Verb	Adverb
common carrier	Yes	No	No	No
business	Yes	No	No	No

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

common carrier: a person or firm in the business of transporting people or goods or messages
business: a commercial or industrial enterprise and the people who constitute it

Other hypernyms of common carrier include business concern, business organisation, business organization, concern.

common carrier (noun)	business (noun)
a person or firm in the business of transporting people or goods or messages	the principal activity in your life that you do to earn money
	the activity of providing goods and services involving financial and commercial and industrial aspects
	the volume of commercial activity
	incidental activity performed by an actor for dramatic effect
	an immediate objective
	a rightful concern or responsibility
	a commercial or industrial enterprise and the people who constitute it
	customers collectively
	business concerns collectively