I've always found that to be quite the hair to split. Quasi-democracy in the narrowly defined homeland and crushing authoritarianism for all other subjects. Separating the UK and the British Empire that way feels like a bit of a fig leaf, a polite fiction.

It's basically the same situation as the USA has w.r.t. the world until maybe very recently, they basically inherited the UK organizational structure.

This sounds like it fails to recognize much of colonial governments, which were typically in the case of the British a very far cry from simply installing an unelected leader or otherwise manipulating leadership through extortion and other means, as the US (among others) is now known to do. There’s an entire wing of cultural, linguistic, and legal imposition that doesn’t seem to exist in what might more accurately be called imperialism by the US, and these changes still have ramifications in how people in the ex-colonies see themselves, their society, and their relationships to the world.

They're quite different things in practice. The US has never had an arrangement like the British Raj in India.