The man referred to himself as a British man and the Scottish guy teased him for it, but that was in 2004 and the speaker was elderly.
I was just considering that any man that is from any country that has English as the national language is an Englishman.
While my "English" (British) friends do refer to themselves as British and have an amazingly strong class system based on local dialect... which carries with it a number of names to describe themselves that are surprising.
On the other hand, a lot of my Scottish friends (that have moved here as teenagers from the UK) have told me that they hate being called part of the British isles or even being referred to as British... So I honestly didn't know.
Granted, they have moved to the US when they were in their late teens and early twenties... so maybe there's the difference. But they have mentioned, hating being referred to as British or to having been part of the British Isles.
And don't get me started on what my Irish friends say about the word "British"...

...there are some things that one just doesn't quote.
As for me, I just would like to know what everyone prefers to be called.