It's not an actual term that is used though. "Great Britain" and "Ireland" are the names of the islands, "the United Kingdom" and "(the Republic of) Ireland" are the names of the sovereign states, "the British Isles" is (one) name for all the bits of land. "British Islands" is not an official term or one that anyone uses.
FYI "British Islands" isn't a specific name whereas all the others are
I’m not sure I follow. It looks as specific in the diagram as all the other names?
It's not an actual term that is used though. "Great Britain" and "Ireland" are the names of the islands, "the United Kingdom" and "(the Republic of) Ireland" are the names of the sovereign states, "the British Isles" is (one) name for all the bits of land. "British Islands" is not an official term or one that anyone uses.