United Kingdom: England, Wales, Scotland, Northern Ireland, isle of Man, Guernsey, Jersey & certain other Channel islands.
Great Britain: the same.
The Irish Republic (the Catholic one) was given indenpendence around 1922 or so.
England is a country & not like a state but the various counties in England function in some manners like our states.
The counties do not have nearly the amount of power that our states have.
Wales has very limited "freedom", but is permitted to use Welsh as the language & English is also spoken there.
Scotland has more freedom than Wales but the Queen is still the ruling symbol.
Norhtern Ireland: is also under direct rule of the Queen & has ongoing violence from the early 1970ies as the majority of Catholics (who are the minority in the north) want to join with the republic.
The Channel islands guerney, Jersey, have a different connction to the UK in that they have certain laws that permit more independence from thecrown & as they are much closer to France they have certain ties sto that country but they are not part of France.
Cornwall the very south western portion of England technically never actually joined as part of the UK although the people there are English but formerly spoke Cornish & had close ethnic ties to the Brittany state of France.
The British military takes in people from all of the UK and also has an Irish guard that comes from the Republic of Ireland. I am not sure how that works but they must defend the Queen & the UK rules while attached to that unit.
Britain has no possessions on the continent of Europe.
They still possess the British Virgin Islands & a few other islands in the Caribbean.
Canada, Australia & new Zealand are considered Dominions of the UK but are independent countries that do accept the Queen as their overall symbol of their dominion but elect their own PM & parliaments.