Since we're on semantics.... Saying someone is "either British or Scottish" is a bit like saying someone is "either American or Californian"
The Britain bit of the UK (full title The United Kingdom of Great Britain and Northern Ireland), is made up of England, Scotland and Wales. So all Scots, Welsh and English are British – whether or not some of them like that fact
So the Scots are unlikely to object if you call them British. Just don't, whatever you do, call them English!
Here endeth today's lesson
A few weeks ago we were having coffee at a local diner, and there were only 2 other tables with customers. A 'mannerless-local-guy' occupied one table, and a family of 4 was seated at the another table. We all struck up a conversation, and as they were tourists they asked about places to visit. They spoke with the loveliest Scottish brogue (is this the correct way to say this?) -- and I could have listened to them talk all day. In the midst of sharing tidbits about places to visit, the 'mannerless-local-guy' said, "Say, are you Brits?" To which the lady rather icily replied, "No. We're Scottish. We live in ..." (and they named their town which I've now forgotten).
The 'mannerless-local-guy' then said, "Well, I thought all you folks were Brits."
Boy-oh-boy, I could have made ice cubes in that room about then.
The Scottish gent was very gracious and shared a brief history lesson with the 'mannerless-local-guy'.
'Twas an interesting exchange.