"The following is a partial list of currently operating independent schools in Scotland. They are referred to as "private schools" in Scotland, common with most of the English-speaking world. The term "public school", used in England to refer to these independently operating schools, is not used in Scotland."

http://en.wikipedia.org/wiki/List_of_independent_schools_in_Scotland

Fair enough it is wiki but there are plenty of other sites to corroborate including the various schools' own sites. The term public school is simply not commonly used in Scotland