These words mean "to cause something not to be open," "to stop or obstruct." Close is somewhat more refined and less blunt than shut. For instance, you might tactfully suggest to a child that he close his mouth while chewing but would say "Shut your mouth" or "Shut up" if you were angry, rude, or annoyed. Signs on public structures are more likely to read "This building is closed on Sunday" than "This building is shut on Sunday." Shut, however, derived from an Old English word related to bolt and shoot, is vigorous and emphatic and should be used when you really mean that something should be barred, bolted, or blocked.
Dictionary of problem words and expressions. Harry Shaw. 1975.