As a brit, its quite amusing to read through some of the comments here where people are effectively trying to nail-down the rules for the identities and relationships between the geographical / political / historical entities that exist inside the British Isles. There seems to be an assumption that there are consensus, unambiguous rules and definitions that structure this stuff - as you'd expect to find in a modern, well-organised state like say the USA or France - but there mostly aren't such things. Not really.

These are very old islands with lots of history. Not everyone agrees on things. What definitions there are are more like leaky abstractions. Living here, you learn that it's necessary to take a relaxed attitude to this stuff.

But, basically, as far as I know...

Geographically:

    British Isles = { Island of Ireland, (island of) Great Britain }

Politically:

    British Isles = { United Kingdom of Great Britain and Northern Ireland, Republic of Ireland, Isle of Man, Channel Islands }

    United Kingdom of Great Britain and Northern Ireland = { Great Britain, Northern Ireland }

    Great Britain = ( England, Scotland, Wales }

    Channel Islands = { Bailiwick of Jersey, Bailiwick of Guernsey }

    Bailiwick of Jersey = { Island of Jersey }

    Bailiwick of Guernsey = ( (islands of) Guernsey, Alderney, Sark, Herm, various small islands }

The British Isles is a geographical entity. The Republic of Ireland and the UK are nation states (aka "countries") in the recognised sense of international law - they have seats at the UN and all that.

England, Scotland, Wales and Northern Ireland are "countries" within the UK. But that meaning of "country" is different to the use of "country" as a synonym for nation state (see above). None of them are nation states. Scotland has a parliament that has extensive legal, political, and financial jurisdiction within Scotland - but the UK parliament (in London, England) has reserved powers over areas like defence and foreign relations. Wales and Northern Ireland have assemblies that are not parliaments but do much the same job as a parliament. England doesn't have a parliament or an assembly, but it hosts the UK parliament in London that legislates for England as well as having final authority over all of the UK (see the problem there?). Scotland of sometimes termed a "nation" and Wales (patronisingly?) a "Principality".

All the parts of the United Kingdom use the pound sterling as their currency. The Republic of Ireland uses the Euro.

There are various problems with all this:

- Geography determines politics determines history.

- The official name for the "Republic of Ireland" is actually "Ireland". Which can sound like island when spoken. I only used the term Republic of Ireland because its impossible to by unambiguous otherwise. Sorry.

- The Island of Ireland (geographical) is not the same as the Republic of Ireland (political) or Ireland (political) and in fact does not map onto a single political entity. Except that its does for people who consider NI to be part of a united Ireland which is an ambition for some but not a de jure thing.

- "Great Britain" is both a geographical entity (the island on the east of the (geographical) British Isles) and a political subdivision (the GB in UK of GB&NI).

- The Isle of Man and Channel Islands are awkward because they're historically and culturally independent and have their own parliaments and laws etc. But they're also kind of "british" in that the UK parliament can legislate for them in extremis, and the UK represents them internationally and at the UN, and guarantees their defence. Also they are "crown dependencies" that are in some squishy sense "owned" by the UK head of state (the Queen) and are dependencies (whatever that means) of The Crown which is the Queen's legal persona/role. Or something like that.

- Scotland and Northern Ireland have their own sterling banknotes, but they're actually printed (issued? both?) by private banks. Elsewhere in the UK the currency is issued by the UK government.

- The traditional/historial provinces of The Island of Ireland (Connacht, Leinster, Munster, and Ulster) are all contained within the Republic of Ireland except for Ulster, which comprises the territory of Northern Ireland and some of the bordering counties of the Republic of Ireland. But "Ulster" is often informally used as a synonym for Northern Ireland. Whether this is correct or just historical probably depends on your political take.

- Northern Ireland is currently "in" (for some values of the word "in") the Eurozone, even though it is part of the UK which left the Eurozone with Brexit.

Its very complicated. This is just my take, and I've probably got many things wrong. Many people will disagree with some of a lot of it, because history|politics|culture. It may possibly offend some (sorry). And thats fine because its complicated.

Edit: NI has local banknotes