Is Great Britain the same as the UK?

No, Great Britain and the United Kingdom refer to different areas.

Great Britain is very often, but incorrectly, used as a synonym for the sovereign state properly known as the United Kingdom of Great Britain and Northern Ireland or the UK for short.

Great Britain is a political term which describes the combination of England, Scotland, and Wales, the three nations which together include all the land on the island. It is also a geographical term referring to the island on which the greater parts of England, Wales and Scotland are situated.

http://www.woodlands-junior.kent.sch.uk/customs/questions/britain/britain.htm