What is the difference between the UK, Great Britain, and England?

These three terms nest inside each other, and mixing them up is a reliable way to annoy a large number of people. England is a single country, one of the four that make up the larger state. Great Britain is a geographic term, it is the name of the island that contains three countries: England, Scotland, and Wales. The United Kingdom (full name: the United Kingdom of Great Britain and Northern Ireland) is the sovereign country, the political state, that includes all of Great Britain plus Northern Ireland, which sits on a separate island. So the UK is made of four countries, England, Scotland, Wales, and Northern Ireland, and it is the entity with a seat at the United Nations, a single government in Westminster, and the passport.

The practical upshot: everyone in England is British and in the UK, but a Scottish or Welsh person is British and in the UK without being English, and calling them English is a genuine insult that treats their distinct nation as an afterthought of the biggest one. Great Britain technically excludes Northern Ireland (which is why UK is the correct term when you mean the whole state), though people, including Brits, use these loosely. Add the further wrinkle that the British Isles is a purely geographic term including the Republic of Ireland, an entirely separate independent country that is not part of the UK at all, and you have a naming system almost designed to trip up outsiders. The safe defaults: say UK when you mean the country and British for its people, use England only for England specifically, and never assume a British person is English.