kitchen cabinet vs coterie

kitchen cabinet and coterie both are nouns.

Word	Noun	Adjective	Verb	Adverb
kitchen cabinet	Yes	No	No	No
coterie	Yes	No	No	No

As nouns, coterie is a hypernym of kitchen cabinet; that is, coterie is a word with a broader meaning than kitchen cabinet:

kitchen cabinet: an inner circle of unofficial advisors to the head of a government
coterie: an exclusive circle of people with a common purpose

Other hypernyms of kitchen cabinet include camp, clique, ingroup, inner circle, pack.

kitchen cabinet (noun)	coterie (noun)
an inner circle of unofficial advisors to the head of a government	an exclusive circle of people with a common purpose