Beginning in 305 AD, the name Lutetia was replaced on milestones by Civitas Parisiorum, or "City of the Parisii"
Great Britain: the biggest island in the British Isles;
England, Scotland, Wales: countries of the UK that share Great Britain;
Ireland: the second biggest island in the British Isles;
Northern Ireland: a country/province of the UK on Ireland;
Republic of Ireland: an independent country that shares Ireland with Northern Ireland.
(The British Isles: All of the thousands of islands in the North Atlantic, including Great Britain and Ireland, that belong to either to the UK or the Republic of Ireland.)
The Crown Dependencies, which are part of the British Isles are part of neither the Republic of Ireland nor the UK. They are "territories for which the United Kingdom is responsible" but do not belong to the United Kingdom. One might say there are five different "countries" making up the British Isles, these being the United Kingdom, the Republic of Ireland, the Bailiwick of Guernsey, the Bailiwick of Jersey and the Isle of Man.
Britons just love to be special and make talking about their different entities a minefield. Similar subjects are city status and the different types of districts of England and especially the combination of the two, i.e. London, which consists of a ceremonial county, Greater London and a sui generis authority, the City of London. Greater London is further split into so-called "London Boroughs", which are not metropolitan boroughs, such as those of the West Midlands and Greater Manchester for example, because that wouldn't be