Even us Brits have trouble with this sometimes. Scotland is a country, just not an independent one, it's part of a larger entity, the United Kingdom; that bit is clear. But our government is called the "British Government" even though it governs the whole United Kingdom, not just the island of Great Britain. Likewise our army is the "British Army" even though it includes the Royal Irish Regiment, and Northern Ireland is not part of Great Britain. So "British" as an adjective seems to mean "of the United Kingdom", rather than "of Britain". It's probably correct in at least some senses to describe the airspace above Scotland as Scottish, British or UK.