From a bit of youtubing and googling the few clips I've heard are instantly recognizable as scottish, with a few words you don't understand.
http://www.bbc.co.uk/news/uk-scotland-north-east-orkney-shet...
http://www.youtube.com/watch?v=Ij60XUvWjZY&feature=playe...
http://www.youtube.com/watch?v=QVxNxnXo7-c&playnext=1...
http://www.youtube.com/watch?v=cx5MgoL5tQ8
The UK has a phenomenal amount of dialects, they're all British though and even a Londoner can tell the difference between a Swedish accent and a British one.
But to your point - a Scottish accent and a Swedish one are distinctly different.
The term British is rather malleable but check the first entry in wikipedia:
http://en.wikipedia.org/wiki/Britain
Yes, common usage of the term British includes the whole of the UK.
The usual problem people from Scotland and Ireland have are being called English, not British and Scots are British anyway and I never mentioned the Irish.
Finally riddle me this, what should I have used instead of British to refer to the people of the UK? Which is where I'm from I might add. As there exists no other term other than British.
http://en.wikipedia.org/wiki/Shetlandic