Common misconception: the United Kingdom belongs to a "group of islands." In fact, the UK is a country that occupies most of an archipelago—the British Isles.
Together, these form the British Isles—a geographical term for the archipelago.
People hear "British Isles" and think "island group the UK belongs to." But the UK comprises most of that group. It's like saying "France belongs to a group of regions called France." The UK is the political entity; the British Isles is the geographical one.
Precision matters: in international law, diplomacy, and Irish/British relations, the distinction between geographical archipelago and sovereign state is non-trivial.