What is the difference between England and Britain (or Great Britain)? Three countries make up Great Britain: England, Scotland and Wales.
So England is part of Great Britain, and a Scotsman (a person of Scottish origin) is British, too. A person born in Wales is Welsh, and they are British, too. Northern Ireland is part of the United Kingdom, or "the UK". So the UK is made up of four countries: England, Scotland, Wales and Northern Ireland, the last of which is not part of Great Britain. The formal name of the country is the "United Kingdom of Great Britain and Northern Ireland", but in everyday speech Britain is often used to mean the UK, though, as you have seen, this is not perfectly correct. The word "great" was added to "Britain" several hundred years ago, in the Middle Ages, when the English kings had lands in what is now France, and a certain part of it was called Britanny. To avoid confusion, they added the word "great" to the name of the land which was larger.