In older times Scotch was an adjective meaning 'of Scotland'. Nowadays the preferred adjective is Scottish or Scots, and Scotch usually pertains to a recipe such as Scotch whisky. The remainder of this article is about the word.
From the early 19th century Scots or Scottish were the preferred usages among educated Scottish people, Scotch being regarded as an anglicised affectation. Scotch is sometimes still used by the working classes who often regard Scots as an anglicised affectation.
In modern English usage the general term for things from or pertaining to Scotland is Scottish. Scots is used for the Scots language and Scots law, although one increasingly hears it used of people and organisations, especially in newspaper articles. Scotch remains in use only for phrases like Scotch broth, Scotch beef, Scotch terrier, Scotch egg, etc. One cynical joke is that Scotch can only be used for things which can be bought, such as whisky, eggs and politicians.
Scotland was the first country in the world to introduce compulsory education, in 1872 (England introduced it in 1880). The Scottish school system was placed under a "Scotch Education Department" with offices in London. In 1918, as a result of objections from within Scotland, the department was moved to Edinburgh and renamed the Scottish Education Department. This reflects the linguistic preferences of modern Scotland.