business vs metier

business and metier both are nouns.

Word	Noun	Adjective	Verb	Adverb
business	Yes	No	No	No
metier	Yes	No	No	No

As nouns, metier is a hyponym of business; that is, metier is a word with a more specific, narrower meaning than business:

business (noun)	metier (noun)
the principal activity in your life that you do to earn money	an occupation for which you are especially well suited
the activity of providing goods and services involving financial and commercial and industrial aspects	an asset of special worth or utility
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