You're right, of course about the UK. It seems that maybe the most accurate (and/or historically appropriate) label for England, Wales, Scotland, and I suppose

You're right, of course about the UK. It seems that maybe the most accurate (and/or historically appropriate) label for England, Wales, Scotland, and I suppose Northern Ireland, are "non-sovereign countries", or more sloppily I guess the UK and England can both be called countries ("a country within a country") with the distinction implied.