It all gets complicated with the names, Wolfgang. Strictly speaking there is no political entity "Great Britain" or even "Britain" for that matter.

No part of Ireland has ever been part of Great Britain, hence the term "United Kingdom of Great Britain and Northern Ireland", or before that "Great Britain and Ireland". I don't think any native of Northern Ireland would describve themselves as a Brit, however Loyalist or Unionist they might be.

The term "Great Britain" refers to the big island, and its various attached smaller islands like the Isle of Wight and Anglesey and the Scottish ones, but never the Isle of Man, nor the Channel Islands, which in theory have no real link with the Westminster government, but only with the Crown, a bit like Canada etc,).

"Great Britain" is essentially a geographical rather than a political term, and means the same as Britain. I've always understood that the Romans just called it Brittania, and that the "Great" bit is to distinguish it from Brittany.