The UK is technically a Kingdom, and includes the entire commonwealth. Canada was part of it until 1967 or so (that meant the Queen had to approve all of its new laws, though the veto power was never used), and Australia still is, having recently voted against breaking away. But Australia, India and other commonwealth countries have separate UN representation, passports, etc.
Northern Ireland is actually a disputed area, with Ireland (until last year) claiming it and thus giving its residents Irish citizenship, even though the UK gives them British citizenship. It has its OWN soccer
team (competing against both Ireland and England) though its players could choose to play for Ireland.
The monarchy has turned over control of the country to Parliament. The UK has no written constitution, but Parliament approved a measure giving Scotland its own legislature
for local matters (crime, education) but they are one country in foreign policy and have one currency. Its analogous to US states having local autonomy, though the US is one country.
Incidentally, Americans (even before the grant of home rule by the British parliament)
frequently referred to Scotland as a separate nation, refer to the UK as “England” (in US history, the nation is ALWAYS called England, even though the Act of Union had already occurred; schoolchildren are never taught that the revolution was fought vs. UK or Great Britain), and sometimes call the nation “Great Britain”.
Incidentally, England and Scotland compete separately in the Miss Universe contest, like they do in soccer. Miss Universe is a US based company. The Miss World contest, based in Britain, has one representative from the UK.
Interestingly, the US has a similar dichotomy with Puerto Rico–separate Olympic teams and Beauty contestants, but they are US
citizens and have no separate UN representation or passports.