The remnants of British colonialism left behind a number of complex citizenship situations, including special types of passports issued to non-citizens, such as the British National (Overseas) passport.
Wikimedia Commons: Hoising (Note the lack of the words "European Union" on the cover, as such passports do not grant EU citizenship rights)
These passports do not grant the right of abode in the UK. While hundreds of thousandsmillions of these passports were issued after the handover, far fewer are in use today, as cheaper Hong Kong SAR passports are often more advantageous.
According to this Freedom of Information request, there are also a number of passports outstanding for British Overseas Territories Citizens, British Overseas Citizens, British Subjects, and British Protected Persons. All hold some form of British nationality, but not British citizenship, and special rules apply to where and how these passports are accepted.
Such situations could lead one to complete your booking form by specifying the UK as their country of passport, but another country as their country of citizenship.