The Sazerac is a local variation of a cognac or whiskey cocktail originally from New Orleans, named for the Sazerac de Forge et Fils brand of cognac brandy. The drink is most traditionally a combination of cognac or rye whiskey, absinthe, Peychaud's Bitters, and sugar. The cocktail, which is a close cousin to the Old Fashioned, has been kicking around in one form or another since as early as 1838 and was trademarked in 1900 by Sazerac Co.
A champagne cocktail is an alcoholic cocktail made with sugar, Angostura bitters, Champagne, brandy and a maraschino cherry as a garnish. A recipe for the cocktail appears as early as "Professor" Jerry Thomas' Bon Vivant's Companion (1862), which omits the brandy or cognac and is considered to be the "classic" American version. It is also one of the IBA official cocktails.