Canadians aren't Americans in a sense of "citizens of USA", but in geographical sense they are. The same applies here.

Using a specific definition of a word to tell people they’re wrong about their own identity usually doesn’t go over very well.

“British” almost always means “identifies with the UK”.

Your link is broken. Are you able to provide another one?

What do they put on a form when asked their nationality? Last time I checked my passport says "British".

I always put Scottish. British would also be acceptable.