brain trust vs coterie

brain trust and coterie both are nouns.

Word	Noun	Adjective	Verb	Adverb
brain trust	Yes	No	No	No
coterie	Yes	No	No	No

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

brain trust: 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 brain trust include camp, clique, ingroup, inner circle, pack.

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