Great Britain is the official name given to the two kingdoms of England and Scotland, and the principality of Wales. The United Kingdom (UK) includes these areas as well as Northern Ireland. Britain refers to only England and Wales, though some will shorten Great Britain with this term.
The Queen's official website disagrees on the corgis (two Corgis: Holly and Willow and two Dorgis: Candy and Vulcan. ohmygod Vulcan) But I just really enjoy that all 11 presidents are represented by a picture of Obama.