The map above shows the United Kingdom. The United Kingdom includes the coloured areas of England, Wales, Scotland and Northern Ireland.
The correct full name for the United Kingdom is the United Kingdom of Great Britain and Northern Ireland.
Great Britain is the name given to the region that includes just England, Scotland and Wales. It doesn’t include Northern Ireland. Great Britain isn’t a county, it’s an island.
United Kingdom = Great Britain + Northern Ireland
Great Britain = England + Scotland + Wales
The United Kingdom is defined as a sovereign country. A sovereign country is a political entity represented by one government, in this case the UK government is based in London in the Houses of Parliament. The UK government has granted the constituent countries of Scotland, Wales and Northern Ireland to have their own regional governments with varying amounts of power although ultimate authority still remains with the UK government based in London.
The Republic of Ireland is a separate country outside of the United Kingdom. It is sometimes referred to as Southern Ireland and its capital is Dublin. More often than not the Republic of Ireland is simply referred to as “Ireland” which is confusing because Ireland is actually the name for the entire island made up of the Republic of Ireland and Northern Ireland (which is part of the United Kingdom).
If you go to an official list of countries in the world, such as the United Nations list, you will find only the United Kingdom (officially the United Kingdom of Great Britain and Northern Ireland) and Ireland (the Republic of Ireland) listed as sovereign countries. England, Scotland, Wales, and Northern Ireland are not listed separately as independent countries, although they are often referred to as countries within the UK for cultural and historical reasons.
The British Isles is the name given to the two islands of Great Britain and Ireland. Hence the British Isles includes England, Scotland, Wales, Northern Ireland and the Republic of Ireland (Southern Ireland) as well as The Isle of Man, The Isles of Scilly, The Channel Islands (including Guernsey, Jersey, Sark and Alderney), as well as many smaller islands.