We have so many different terms that everyone may as well give up.
You've got England, Scotland, Wales and Northern Ireland. They're all countries, but have a single centralised government housed in London. (Some powers are now devolved to the constituent countries)
You've got Great Britain - which is England, Scotland and Wales.
You've got the UK - which is England, Scotland, Wales and Northern Ireland.
You've also got the British Isles - Which is a purely geographical term for Great Britain and ALL of Ireland. It's a term that Ireland now refuses to recognise.
Many of the people that live in the UK could not tell you the difference, so why should I expect anyone else to?