This is generally the source of much confusion. Even amongst those who live over here. If you look carefully at the description of the United Kingdom you’ll see it’s the United Kingdom of Great Britain and Northern Ireland. And the British Isles is the group of islands as a whole including all of Ireland too.
The source I liked best for this explaining this and much more, was Project Britain.
For much further confusion, think for a moment why there’s a UK passport, Great Britain in the Olympic games, and in football we compete as England, Wales, Scotland and N. Ireland separately. 🤔