The Great British Venn Diagram should clear up some confusion:
The Republic of Ireland and the United Kingdom are the only two sovereign states in this image. They are shown in red. Ireland and Great Britain are both islands and are shown in green. England, Scotland, Wales and Northern Ireland are constituent countries of the United Kingdom and are shown in orange.You have the basic idea. There are many other islands in the British Isles which are not shown here. Most of these are politically part of England, Scotland, Wales, Northern Ireland or the Republic of Ireland, with the exceptions of the Isle of Man and the Channel Islands, which are British crown dependencies and not part of the UK (or ROI) at all.
There are some complications though:
The UK’s full name is “The United Kingdom of Great Britain and Northern Ireland”. People from the UK are called “British”. One British person is called a Briton.As “British” can be used to mean “of or pertaining to the United Kingdom”, people from the Republic of Ireland often object to calling the whole kaboodle “The British Isles”, as the ROI isn’t actually “British” in that sense. However, there is no consensus on what to call it instead. (May I humbly suggest “The British and Irish Isles”?)
England, Wales, Scotland, Northern Ireland and the Republic of Ireland frequently field separate teams in such sports as rugby, football (i.e. the World Cup), cricket and so on. This is largely because our various nations have been playing rugby, football and cricket for longer than the UK has existed.
Lastly, to be pedantic, this is actually an Euler diagram, not a Venn diagram.