Gill links to Sam, who’s rendered a handy, dandy Venn diagram that clarifies the difference between British Isles, Great Britain, the United Kingdom et al. Sam lives in the British Isles, so she ought to know.
Of course, things get kind of complicated in Northern Ireland. At least half of those folks would disagree with them being the union intersection (math, it ain’t my strength) of Ireland and the UK.
In an offline discussion about which dots are countries, my friend Karl confuses matters:
That depends on how you define “country”! Scotland & Wales – and
sometimes Northern Ireland – have a devolved government with lots of
local responsibility. Scotland & N. Ireland (dunno about Wales) have
their own banknotes and police forces. But the tax is collected
centrally and controlled by the UK government. Everyone in the UK can
vote representatives into the UK parliament. The defense forces are
controlled by the UK department of defense.So if a country is an entity that collects & spends its own taxes, has
a government and an army, then the UK is the country. But if a country
is an entity with a soccer team – a much more valid definition, really
– then Scotland, Wales, England, Northern Ireland and the Rep. of
Ireland are countries.Of course, if you’re a rugby fan, then the countries are Scotland,
Wales, England and Ireland (north & south).
DarrenBarefoot.com 
“At least half of those folks would disagree with them being the union of Ireland and the UK.”
So they should. Intersection, not union, right?
— Rob “I Was On The School Pedantry Team” C.
AND != OR.
Intersection is correct.
I’ll also note that there are a few people in Scotland and Wales that would disagree with those countries being placed in ‘Great Britain’.
If socc– I mean football teams are all you need, then Manchester and Liverpool are separate countries, right?
That diagram is very inaccurate. Republic of Ireland is not part of any “British Isles”. If Sam removes the largest surrounding circle in the diagram then he has an accurate venn diagram. The current one is wrong.
Sean is correct. Ireland is not part of the British Isles. Every generation of Irish men and women fought to re-establish sovereignty over their own lands for 800 years to prevent establishing any validity in the term “British Isles”. It is correct to say the British Isles and Ireland. I’m not a bit sectarian, but I’m not British, and the land I live in, and the culture I grew up in aren’t either. Our cultures are fundamentally different.