When used to refer to any generic alcoholic mixed drink, cocktail may mean any beverage that contains two or more ingredients if at least one of those ingredients contains alcohol.
When a mixed drink contains only a distilled spirit and a mixer, such as soda or fruit juice, it is a highball; many of the International Bartenders Association Official Cocktails are highballs. When a cocktail contains only a distilled spirit and a liqueur, it is a duo and when it adds a mixer, it is a trio. Additional ingredients may be sugar, honey, milk, cream, and various herbs.