The United KingdomorGreat Britain?
Great Britain is the term used for the island containing the contiguous nations¹ of England, Scotland and Wales. Great Britain is used to distinguish Britain from Brittania Minor, or Brittany, in France. The term "Great Britain" was officially used only after King James I (who was also James VI of Scotland) acceded to the throne of England and Wales in 1603, styling himself King of Great Britain, although legislative union between Scotland and England did not take place until 1707.

England, Scotland and Wales together with the province of Northern Ireland, form the country officially known as "The United Kingdom of Great Britain and Northern Ireland" or simply the United Kingdom.
The United Kingdom came into being in 1801 following the Irish Union, although the greater part of Ireland gained independence in 1921 to form the Irish Republic (or Eire). The majority of the people in Northern Ireland have wished to remain part of the U.K., although a minority wish unification with the Irish Republic.
The term "England" is sometimes erroneously used by both natives of England (the English) and those outside our country to refer to the United Kingdom. Natives of the other constituent nations of the U.K. find such usage offensive, so it is best avoided! Although there is no adjective for the "United Kingdom" the term "British" is acceptable, although has to be used with care and sensitivity in Northern Ireland, where one section of the community would be happy being so-described, whereas the other would most definitely regard themselves as "Irish".
The United Kingdom does not include the Isle of Man (which lies between Great Britain and the island of Ireland) and the Channel Islands (which lie off the North coast of France). These are direct dependencies of the British Crown, maintaining their own legislative, monetary and taxation systems. Each have their own parliaments and a Governor, appointed by the Crown.
The British Isles is used more loosely to describe the main island of Great Britain together with its associated islands (including the Isle of Man). It has no legal significance.
The Channel Islands, which include the independent States of Jersey, Guernsey, Alderney and Sark, are the only remaining components of the "Duchy of Normandy" which still belong to the British Crown.
The United Kingdom (including the Channel Islands, but without the Isle of Man) is a member of the European Union. The Isle of Man maintains free-trade agreements with the EU, but is not a member.