If you think it's hard (for us) to understand the definition of 'British', have some sympathy for foreigners.
A few years ago, in the US, I shared a taxi to the airport with a seemingly well-educated and intelligent US native. It was just after St Patrick's day, which they make a big thing of, and he asked to clarify the differences between Irish, Scottish, English and British.
By the time I'd explained that Ireland is comprised of a politically very different North and South, and that Scotland is not part of England, and neither is Northern Ireland or Wales, yet the 'United Kingdom' is that of 'Great Britain and Northern Ireland', as opposed to of 'England, Scotland, Wales and NI'... well, I could sense the poor man's head was in quite a spin. In fact, so was mine.