The United Kingdom vs Great Britain

Status: September 2003

"The nation of Great Britain (usually shortened to Britain) is made up of tree countries: England, Wales and Scotland. The United Kingdom (UK) consists of Great Britain, Northern Ireland and some semi-autonomous islands such as the Isle of Man and the Channel Isles. The island of Ireland consists of Northern Ireland and the Republic of Ireland. The latter, also called Eire, is a completely separate country to the former. The British Isles is a geographical term for whole group of islands that make up the UK and the Republic of Ireland."
Britain, Lonely Planet Publications, 5th edition, March 2003, ISBN 1-74059-338-3

GREAT BRITAIN
[n]  an island comprising England
     and Scotland and Wales 
UNITED KINGDOM
[n]  a monarchy in northwestern Europe
     occupying most of the British Isles;
     divided into England and Scotland
     and Wales and Northern Ireland

"Country name - conventional long form: United Kingdom of Great Britain and Northern Ireland
conventional short form: United Kingdom
abbreviation: UK
... the current name of the country, the United Kingdom of Great Britain and Northern Ireland, was adopted in 1927"
The World Factbook, CIA, 2003

Conclusion

The United Kingdom (United Kingdom of Great Britain and Northern Ireland) is the officially recognized state. Great Britain is a part of the United Kingdom.