SNG:
Hope this helps:
- English folk are English, British and from England and the UK.
- Scottish folk are Scottish, British and from Scotland and the UK
- Welsh folk are Welsh, British and from Wales and the UK
- Some Irish folk are Irish, British and from Northern Ireland and the UK
- The majority of Irish folk are Irish, from Ireland / Southern Ireland / Eire (a whole other country) and are not British or from the UK
- Only folks from the part of the UK that is called England are English. All others have their own respective countries within the union (a common American mistake, when dealing with Scots, etc., that is almost guaranteed to cause outrage)
You might call yourself British, but you'd never call yourself a United Kingdomer.
You might, however, say that you were from Britain or the UK.
I might refer to myself as a Brit, when talking to folks from the US, just because it's easier.
Just to compound matters, we're also European (though the UK isn't part of the European monetary union, but I believe that Ireland is).