"United Kingdom" is the short version. The full name is "United Kingdom of Great Britain and Northern Ireland". So from this you can deduce that Great Britain is the part of the UK that is not Northern Ireland.

Great Britain refers to England, Scotland and Wales (the island essentially) The United Kingdom or UK refers to immediate territories outside of the island such as Northern Ireland, along with England, Scotland and Wales. To go one step further, the British Isles refer to the UK + Republic of Ireland. Regards, M