I read up on this topic prior to a recent-ish trip across the pond. The goal was to not appear to be an ignorant American, though I don't think it was achieved.

Great Britain is the name of the island on which the countries of England, Scotland, and Wales reside. The United Kingdom is a sovereign state comprised of these countries plus Northern Ireland and many smaller islands. So GB refers to geography and UK to the political organization. That said, people tend to use GB or just Britain to refer to the government as well. So the context in which the term is used is important.