This morning, my mother-in-law told us how she just recently learned that Scotland is not a country, but is part of the country Great Britain. I told her that I was surprised too when I learned this a few years ago.
In my previous job, I had the opportunity to spend time in Nottingham and London in England and Edinburgh in Scotland. While I was there, I told people that I didn't understand the difference between the United Kingdom and Great Britain and how they were related to England, Scotland, Wales, Ireland, and Northern Ireland. I always thought that England, Scotland, Wales, and Ireland were their own countries. They were probably thinking: typical American :)
Now I know that the United Kingdom is its own country composed of England, Scotland, Wales, and Northern Ireland and Ireland is its own separate country. Great Britain is an island consisting of everything in the United Kingdom except for Northern Ireland. The U.K. is actually short for the United Kingdom of Great Britain and Northern Ireland.
The Wikipedia, as usual, explains each of these areas: