Why is Northern Ireland part of the UK but not part of Great Britain?

BRITAIN is an island, on which are found England, Scotland and Wales. Round its coasts are a number of other islands - the Isle of Wight, the Scottish Isles and so on - and this collection of islands is GREAT BRITAIN. Ireland is a separate land mass. Until Irish independence, the British monarchs ruled over the United Kingdom of Great Britain and Ireland. When Ireland finally managed to break away, six counties in the North remained loyal to the United Kingdom, which then became the United Kingdom of Great Britain and Northern Ireland.

There is another anomaly, the Channel Islands, which are closer to France than to England, and constitute all that remains for the Duchy of Normandy: they are ruled by the Crown, but not part of either the UK or of Great Britain.