That is confusing because the word 'country', along with 'nation', 'state', 'republic', 'province', 'region', 'county', 'department' and many others are not well defined and are used in different ways in different countries....
In the American and Australian systems, we use the word “state” for provinces. This slightly conflicts with the definition of a sovereign state, but we’re usually okay with that.
In the UK, we use the word “country” for our provinces, for somewhat obvious historical reasons. This conflicts with the legal definition of a country that the League of Nations set out, and the UN adopted - but we’re usually okay with that.
So we have a nation named the United Kingdom (of etc etc), which meet the legal definition of a sovereign state. And this nation is composed of four countries, which meet the definition of a country in the English language - but not in international law.
Most of England, Wales and Scotland make up Great Britain. Northern Ireland and the Republic of Ireland make up Ireland. Together Great Britain and Ireland make up the British Isles, and it's Great Britain and Northern Ireland that make up the United Kingdom.
United Kingdom (UK) comprises four countries: England, Scotland, Wales and Northern Ireland..