People often say Britain or Great Britain when they mean the United Kingdom. Whether this is just common useage or plain wrong I guess depends on your perspective. Even the Olympic team from the United Kingdom is called "Great Britain", which some people think is fine, and other people think is wrong or stupid or both. Because strictly speaking "Great Britain" notionally excludes people from Norther Ireland, and other islands, that compete as part of the "Great Britain" team.
Incidentally the term "Great Britain" was originally intended to distinguish the island of Britain from the smaller region of France called Brittany. It was not intended to imply "greatness" as such, imperial or otherwise, as some have taken it mean; most commonly as in the embarrassing phrase: "Britain didn't become 'great' by... accepting orders from Brussels", or whatever else the person has a bee in their bonnet over.