As an actual Scot it's definitely standard for some things: Scots law, Scots pine. Wikipedia says:

"The use of "Scots" and "Scottish" is not altogether consistent; but in most words and phrases referring to Scotland's people one or the other is normally used: there is a certain tendency for "Scottish" to be used in more formal contexts."

https://en.wikipedia.org/wiki/Scotch_(adjective)

Edit: There is probably absolutely no sensible reason why it is Scots Law but the Scottish Government.