"Great Britain" is interchangeable with "United Kingdom of Great Britain and Northern Ireland" by dint of the OED, custom and practice and common language. The technical difference is not one that upsets people, not even Ian Paisley and his band of bigots. Th reason being there is no statutory body that deals with just Great Britain, it is technically the mainland island rather than describing the three countries within or the countries without. If you were to be pedantic, you would have to include Isle of Man, Isles of Scilly, all the Channel Islands...
A bit like saying United States and Commonwealths of America, or plain USA, or even Dumbfuckistan.