This 'article' was originally just a proposal. It has now been made 'official' by moving it to British Isles (terminology). I gathered all this info from various articles (see talk page). I've linked to this page from various talk-pages, just to get the discussion (if any - I hope) going. The idea is to make this text into an article. Apart from linguistic errors, it might be handy if you don't alter the article yet. Please read the discussion first and add your comments there.
There are various different and similar terms relating to partly overlapping geographical and political regions. The main things to know are
Although one can (and does) split hairs over these definitions. Even authoritative sources (government and encyclopedias) disagree and even contradict themselves.
In more detail (for those who can stomach it):
Geographically, there are two Britains. One is Brittany (which might mean 'Little Britain'), a historical term for a peninsula in France that largely corresponds with the present day French province of Bretagne. The other is Great Britain, the largest of the British Isles, a group of islands in the Atlantic Ocean off the coast of Continental Europe. The second largest island is Ireland. And then there are many more islands, for a total of 1098.
Politically, the British Isles comprise the Republic of Ireland (the larger part of the island of Ireland) and Great Britain, which comprises England, Wales and Scotland (in Britain) and Northern Ireland (in Ireland). The United Kingdom is short for The United Kingdom of Great Britain and Northern Ireland, which makes it self-explanatory. The term British Islands (as opposed to British Isles) is another official name for the UK since 1978. The UK is a country, but so are England and Scotland. Northern Ireland is a province. And Wales is a principality (the prince of which is really just the king of the UK to be, who has nothing to with Wales). These four are also know as Home Nations (though Northern Ireland is also sometimes said to be one). The British Isles also comprise the crown dependencies Isle of Man and the Channel Islands (Guernsey and Jersey). Neither of these are part of the UK, though. Culturally, the Cornish are distinct from the English, but politically the duchy of Cornwall has the same status as any other county in England.
So Great Britain (which might be taken to mean Big Britain) is both a geographical and a political entity. Geographically, it is one island, but politically it also contains the islands that are part of it's constituent parts England, Wales and Scotland (most notably Scotland's Hebrides, Orkney Islands and Shetland Islands). Also, politically, it contains two countries and a Principality, but is not a country itself. However, the abbreviation GB is sometimes officially used for the UK (eg in the Olympics and as the vehicle identification code) and citizens of the UK are called British, Britons or Brits (which are actually incorrect, but the alternative would have to be something like UK'ians). Slang names for Britons are Pom and Tommy (for British soldiers) and Limey. The term Anglo, historically meaning 'English' is sometimes used as a prefix, as in Anglo-French relations, although that is also incorrect because it is used to refer to the UK rather than just England.
Ireland is also known as 'the Emerald Isle'. Naming in Ireland is often a political issue. First off, some Irish (who don't regard themselves as British) object to the geographical term 'the British Isles' and prefer the term Islands of the North Atlantic or simply 'Britain and Ireland'. The Republic of Ireland is also known as 'the Twenty-six Counties', as opposed to 'the Six Counties', which form Northern Ireland, a name that avoids the disputed link with Britain. Some even call it 'the occupied six counties', for obvious reasons (some even criticise the name 'Republic of Ireland' because that should encompass all of Ireland). A better known name for Northern Ireland is Ulster, although, strictly, that also includes three provinces of the Republic of Ireland. This name and 'the Province' are preferred by Unionists because they suggests an origin older than 1922 (the idea that it already existed as an entity a long time ago). There are even political disputes about the distinction between the names 'Northern Ireland' and 'the North of Ireland'. And placenames also come into play; see Derry/Londonderry name dispute.
Historically, the Greeks called Britian Pretaniké and the Romans called their province on the island Britannia (which covered roughly the same area as present-day England and Wales), Scotland Caledonia and Ireland Hibernia (which they never managed to conquer). In 1536/1543 England and Wales united (though effectively Wales joined England; the name England is still often used to mean Wales as well and the laws are largely the same) into the still existing unity England and Wales. After centuries of English influence in Scotland, in 1603 the Scottish king James VI inherited the English throne and in 1707 the Kingdom of England (now including Wales) and the Kingdom of Scotland ceased to exist when they united into the (United) Kingdom of Great Britain. In 1801 the Kingdom of Ireland (the throne of which was already held by the English king) was also added, changing the name to the United Kingdom of Great Britain and Ireland. In 1922 most of Ireland split off again to form first the Irish Free State (a constitutional monarchy) and then in 1937 the Republic of Ireland (which finally changed the full name of the UK to what it is today: the United Kingdom of Great Britain and Northern Ireland). Scotland and Northern Ireland have more independence than Wales and in 1999 Scotland even got its own parliament.
British overseas territories have (or have had) various relationshops with the UK, such as Bermuda, Gibraltar, Hong Kong and the British Arctic Territory. The Commonwealth of Nations (formerly the British Commonwealth) is a loose confederation of nations roughly corresponding to the former British Empire, mostly for economic cooperation, formalised in 1931. The Commonwealth of England has nothing to do with this and was a temporary republic, replacing the UK, under Oliver Cromwell, from 1649 to 1660.
Linguistically, there are the Celtic names Éire (Ireland, but also used for just the Republic) Uladh (Northern Ireland), Alba (Scotland) and Cymru (Wales).
Oh, and then there's the matter of whether these islands, being islands, are really part of Europe ('the Continent'), but let's not get into that....