All three of these words may be defined, as an adjective, as “of or relating to Scotland or its people,” and as a noun as “the Scots language,” but in modern usage, the words have different connotations. In fact, some people from Scotland may take offense if you refer to them as Scotch.
Scottish is the preferred adjective; when referring to the people, culture or ancestry of the people of Scotland, it is generally correct to describe them as Scottish.
Scots is most often used to refer to the dialect of English found in Scotland.
Scotch is generally used as an adjective to refer to certain food products, such as Scotch pie, Scotch broth, Scotch eggs or Scotch whisky (spelled whiskey in American English.)
For more background, read about these words on The Grammarphobia Blog.
Updated March 2024