The UK's full official name is a long one: the United Kingdom of Great Britain and Northern Ireland. In everyday life people just say "the UK".
The "Great Britain" in that name covers only England, Scotland and Wales. It does not include Northern Ireland. So Great Britain and the UK are not the same thing:
UK = Great Britain (England + Scotland + Wales) + Northern Ireland
The "Great" in Great Britain is not a boast. It is closer to "the bigger one". In the 2nd century AD the Greek geographer Ptolemy called the larger island "Great Britain" and the smaller one, Ireland, "Little Britain". In the Middle Ages the name also helped tell Britain apart from Brittany, across the Channel in France, whose name has the same root and which was once known as "Little Britain" too. So Great Britain really means "the big island of Britain", not "glorious Britain".
And what about "Britain" and "British"? The handbook makes a special point here: in its pages, the words Britain, British Isles and British all mean all the people of the UK.
Boxes inside boxes: Great Britain is inside the UK, and the UK is inside the geographical British Isles. The Crown dependencies and the Republic of Ireland are in the British Isles but not in the UK. The overseas territories are scattered around the world.
How did the name get so long?
The UK did not always have such a long name. Every time a new member joined, or a piece of land left, the name changed with it:
1707England (which by then included Wales) and Scotland join together to form the Kingdom of Great Britain
1801A union with Ireland creates the United Kingdom of Great Britain and Ireland
1922The south of Ireland leaves the UK as the Irish Free State; the north stays and becomes Northern Ireland
1927The UK Parliament passes a law changing the name to today's United Kingdom of Great Britain and Northern Ireland
You can read about the unions of 1707 and 1801, and how Ireland was divided, in the History topic, under A Global Power and The Two World Wars.
Quiz
Which countries make up Great Britain?
Great Britain is just three: England, Scotland and Wales. C is the whole UK, which also includes Northern Ireland. The most common trap in this question is treating Great Britain and the UK as the same thing.
Quiz
Complete the official name of the UK: "The United Kingdom of …"
The official name ends "of Great Britain and Northern Ireland". B, "the United Kingdom of Great Britain and Ireland", was the name from 1801 to 1922, when the whole of Ireland was in the UK.
Quiz
Is the statement below TRUE or FALSE?
Northern Ireland is part of Great Britain.
False. Northern Ireland is part of the UK, but it is not part of Great Britain. Remember the row over the name "Team GB": the UK's Olympic team includes athletes from Northern Ireland, which is not in Great Britain.