Couple of corrections/quarrels/nitpicks as regards jjimm’s analysis.
Geographically, we have
Great Britain, an island, and
Ireland, an island
Policitally, we have a rather more complex situation.
The United Kingdom of Great Britain and Northern Ireland, often referred to as Britain, is a multinational state which consists of
(a) Great Britain, which in turn comprises England, Scotland and Wales (each of which is a country, with Wales occasionally being called a principality as well), and
(b) Northern Ireland, which is variously called a “country”, a “province”, a “state” or something else, depending on your political views. It has no official legal description other than its name.
And we also have Ireland, a separate state which has the same name as the island of Ireland, but which covers only part of the island. The description of the state, adopted in 1948, is “the Republic of Ireland”, but the name, adopted in 1937, is “Ireland”. The description is used where confusion with the geographic island of Ireland might otherwise cause confusion.
Yojimboguy asks about “affiliates”, by whih I take it he means countries which are affiliated in some way to the UK.
The British Empire ceased to exist in 1947, when India achieved self-government, and George VI ceased to be emperor. What there is now is the Commonwealth of Nations, an association of independent states, of which the UK is one. The Queen of the UK is the head of the Commonwealth, although she is not the head of state of most of its member states. Most of the states which are members of the Commonwealth were at one time colonies or protectorates of the UK, but not all. Most of the former colonies or protectorates of the UK are in the Commonwealth, but not all. Ireland is not a member of the Commonwealth.
India is a member of the Commonwealth.
“Dominion” is the official description of the state in Canada and New Zealand and, by extension, came to be used as a label for those former British colonies which achieved self-governing status, but retained the British monarch as head of state. In that context its not a term which has much political signficance nowadays.