Great Britain is the name of an island – an island which is comprised of most of England, most of Wales, and most of Scotland.
I live on Great Britain, though I was born and raised on a neighbouring island which is named Ireland. Specifically, I was born in that part of Ireland known as Northern Ireland.
Northern Ireland, Great Britain, and their many and various offshore islands make up the state in which I have always lived, the United Kingdom of Great Britain and Northern Ireland.
There is no state called Great Britain.
I trust this is entirely clear (!).
See British Isles (terminology) at Wikipedia.