Formerly, "Scotch" was used as an alternative for "Scots" or "Scottish". The current convention is as follows:
"Scottish" for most purposes, including people, animals, and things in general.
"Scots" also for people, and for identifiably human matters and institutions (e.g., the Scots, Scotsmen; Scots Law (capitalized); the Scots language, which is never "the Scottish language"; rarely Scots culture, which is more commonly Scottish culture). It appears in combining form in Scots-Irish. The Scots pine is named after Scotland, though not limited to it.
"Scotch" is sometimes (and decreasingly) used for foods produced in Scotland (e.g., Scotch salmon, Scotch tomatoes; more commonly Scottish), and always for Scotch whisky (never "Scottish whisky"). It also appears in Scotch bonnet, Scotch egg, Scotch broth and the scotch doubles tournament format (which is usually lower-cased); and in the Scotch Game or Scotch Opening in chess. Scotch is otherwise best avoided, especially as applied to people, as Scots themselves consider it offensive, including the archaic Scotchmen and Scotchwomen.