Brain trust is a North American term for a committee of persons who are in charge of advising someone about planning and strategy. This can be official or unofficial and is usually used in the realm of politics and governments.
The noun for a person in this group is a brain truster.
Outside the US, the term is brains trust and signifies a group, usually experts in their occupations, who field questions in a forum, either on the radio or in person.
The noun form for a person in a brains trust is brains truster.
A think tank is a group of people, usually experts, who come together to brainstorm ideas for solutions to various problems. They share their solutions with the public at large and usually not a specific organization or person. Think tanks are generally concerned with large political or economic issues.
A person in a think tank is a think tanker.
At the Boston meeting last week, Romney’s brain trust gave him a clear-eyed assessment of his chances in 2016, with some aides chiming in via conference call. [CNN]
“They constitute a kind of brains trust of eminent scientists who are able to provide advice to policy-makers that is independent, free of vested interests, subject to peer review and evidence-based.” [University World News]
Last month, a Chinese government think tank bashed history professors from Harvard, Georgetown and other leading American universities regarding things they wrote — at least 15 years ago — about events that occurred more than two centuries ago. [NPR]