Technicality, British can refer to both the entirety of the British Isles, although that’s rarely ever how it’s used, and the island of Great Britain, how it’s more commonly used. Unfortunately, where I live in the United States, we tend to think Great Britain just means English. Which, is a bit weird, given the word Brit is a Celtic word and not a Germanic one. I had a professor that is from Scotland, she refers to herself mostly as Scottish, but was not offended by being called British, and said that when she lived in France they drove the point that she was British home. She often does call herself British, and says she’s very British. I’ve seen some Scottish nationalist that don’t like being called British, but again I don’t understand that, because Great Britain is still the name of the island either way. That said, I can completely understand why you shouldn’t call Scottish and Welsh people English.