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Euler diagram of the terminology of the British Isles
(lemmy.sdf.org)
Apologies. This might not be the perfect community for the post.
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.