The meanings of Britain and British have evolved over time and as they have gained political significance.
In 325 BC the Greek Pytheas of Massalia visited a group of islands which he called Pretaniké, the principal ones being Albionon (Albion) and Ierne (Erin). (The records of this visit date from much more recent times, so there is room for these details to be disputed.) To linguists, this suggests the Brythonic inhabitants called themselves Priteni.
When the Romans took control of the largest island they called their possessions Britannia. The earlier celtic inhabitants became known as Britons and the island as Britain. Some centuries after the Romans had left, some of these Britons migrated to the near continent. About 1000 years later (i.e. by the late Middle Ages) the region they had moved to was known as Brittany, and to distinguish the island the term Great Britain was used (compare the French names Bretagne and Grande Bretagne).
The kingdoms established on the island of Great Britain were perceived to be dominant over the whole archipelago, which had thus became known as the British Isles. In 1603 the kingdoms shared one King, James VI of Scotland and I of England. He proposed unifying the kingdoms under the name of Great Britain. This eventually came to pass in 1707 when the Kingdom of Great Britain was formed. The adjective used for the kingdom was British.
Since its formation, the kingdom was enlarged in 1801 by the addition of the island of Ireland, then reduced, around 1920, by the loss of what is now the Republic of Ireland. The name of the kingdom changed accordingly, culminating in The United Kingdom of Great Britain and Northern Ireland. To some writers the meaning of British and Britain have changed with the Kingdom. The word British is now in common use to indicate United Kingdom (UK) nationality because there is no suitable substitute. However, to other writers Britain is still synonymous with only the island of Great Britain.
Other terms also cause confusion. Great Britain is undisputedly the name of the large island, but is occasionally used to mean the UK, for instance in the modern Olympic Games. The British Isles is still a geographical term for the archipelago, but it can also still be seen as implying dominance by Great Britain, so it is sometimes avoided. The prefix Anglo, usually meaning English, is sometimes used to denote the UK, as in Anglo-Irish. See the respective articles.