Formula One, abbreviated to F1, is the highest tier of FIA-sanctioned, graduated open-wheel Formula racing and is regulated by the Fédération Internationale de l'Automobile (FIA). The "formula" in the name refers to a set of rules to which all participants and cars must conform. The F1 world championship season consists of a series of races, known as Grands Prix, held usually on purpose-built circuits, and in a few cases on closed city streets, the most famous of which is the Monaco Grand Prix in Monte Carlo. The results of each race are combined to determine two annual World Championships, one for drivers and one for constructors.
http://en.wikipedia.org/wiki/Formula_1

Champ Car, was the name for a class and specification of cars used in American Championship Car Racing for many decades, primarily for use in the Indianapolis 500 auto race. Such racing has been sanctioned by the American Automobile Association, the United States Auto Club, the Sports Car Club of America, Championship Auto Racing Teams (CART), the Championship Racing League, the Indy Racing League, and the Champ Car World Series (CCWS).

The Indy Racing League, better known as IRL, is the sanctioning body of a predominantly American based open-wheel racing series. The League consists of two series, the premier IndyCar Series (usually considered synonymous with the Indy Racing League), whose centerpiece is the Indianapolis 500, and Firestone Indy Lights, the official developmental series of the Indy Racing League.