So I guess a lot of people are in some doubt as to what the difference is between England, Great Britain, the British Isles and the United Kingdom. Here I present a handy-dandy Venn diagram to explain this.
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. Here, the term "constituent country" is not used in the same way that "country" is usually used; England, Scotland, Wales and Northern Ireland are political subdivisions of the UK, and it is the UK which appears in international bodies such as the United Nations and NATO.
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.
The UK's full name is "the United Kingdom of Great Britain and Northern Ireland".
"Britain" is not a technically correct term for any political or geographical entity. Nevertheless, "Britain" is in frequent use, and taken to mean either "the UK" or "Great Britain". This usage is pretty unfair to Northern Ireland whichever way you look at it.
The ROI's full name is "Ireland" (if you are speaking English) or "Éire" (if you are speaking Irish).
Ireland is popularly referred to as "the Republic of Ireland" in order to distinguish it from the island of Ireland, and the country is indeed a republic, but "the Republic of" is not part of the country's official name, and I suppose technically this means that the R need not be capitalised.
Citizens of the UK are called "British". One British person is called a Briton.
Citizens of the ROI are called "Irish".
Irish citizens are not British citizens. British citizens are not Irish citizens.
There is no such thing as English, Scottish, Welsh or Northern Irish citizenship. English, Scottish, Welsh and Northern Irish people almost always hold British citizenships.
Of course, anybody, living anywhere in the British Isles or the world, can have any ethnicity, and hold any citizenship.
Many people living in Northern Ireland (which is part of the UK) are citizens of the ROI (which is not part of the UK).
Some citizens of the UK living in Northern Ireland (which is part of the UK) classify themselves as Irish-ethnic.
Some people living in Northern Ireland (which is part of the UK) would even like Northern Ireland itself classified as part of the ROI instead of the UK. This is a contentious point.
The ROI is not British. However, the "British Isles" include both the UK and ROI. Irish citizens and Irish-ethnic people hate this, but there is no consensus on what to call it instead.
England, Wales, Scotland, Northern Ireland and the republic of Ireland often field separate teams in such international sports as rugby, football (i.e. the World Cup) and cricket. Meanwhile, the Irish international rugby team is composed of players chosen from both the ROI and Northern Ireland. This is largely because our various nations have been playing rugby, football and cricket for centuries, whereas the current political arrangement of the British Isles was only established in 1920.
Athletes from the UK (which includes Northern Ireland) compete in the Olympic Games as Team GB, where "GB" stands for "Great Britain" (which does not include Northern Ireland). There is no good reason for this.
The UK's ISO 3166-1 alpha-2 code is
GB, its ISO 3166-1 alpha-3 code is
GBR and its NATO trigram is also
GBR. Again, there is no good reason for these designations. Note that the UK's NATO digram is
Yes. It is called Brittany and it is in northwest France.