Basic geographical knowledge shouldn’t be considered a form of pedantry, especially when it’s your home country in question. The "British Isles" is a geographical term for the archipelago (including Ireland), while the "UK" is a political entity (England, Scotland, Wales, Northern Ireland). The British Isles covers all islands, whereas the UK is just a subset of them; Ireland is geographically in the Isles but is a separate, independent nation.
