I've seen from sources claim that the word "British" can be used to refer to different things. Some say Great Britian, some the UK, and some even the UK including her overseas territories. Which of these is correct? If it refers to people from the whole of the UK (and her territories), then why? It seems natural to assume that only people from Great Britain are British, and I was under the impression that the Britons inhabited what is now known as Great Britain. Here are some examples:
http://www.oxforddictionaries.com/definition/english/British?q=British: "British: relating to Great Britain or the United Kingdom, or to its people or language."
(a poor source, I know, but I've seen it used this way in person)
http://en.wikipedia.org/wiki/British_people: "British people, also referred to as Britons, informally as Brits, or archaically as Britishers, are nationals or natives of the United Kingdom, British Overseas Territories, Crown Dependencies; and their descendants."