Most likely derived from a popular pre-Prohibition drink called The Judge* (two parts brandy, one part crème de menthe and simple syrup), The Stinger is a "duo" cocktail. A duo is a drink that contains only a liqueur and a spirit, with the liqueur acting as a cocktail sweetener. (FYI: If a creamy element is added a cocktail is a "trio".)
The Stinger is a classic cocktail with some fun Hollywood history. In the 1957 film Kiss Them For Me, Cary Grant and Jayne Mansfield were drinking them. Grant seemed to have enjoyed the Stinger because he also enjoyed one in the film The Bishop's Wife.
The Vodka Stinger even has starring role in a song line, "...Another chance to disapprove, another brilliant zinger. Another reason not to move, another Vodka Stinger!" from the Sondheim song Ladies Who Lunch.