"Grand Prix" is a somewhat generic term applied to certain auto races (and, for that matter, tennis matches and other sports), while F-1 (Formula 1) refers to cars built to the specific rules to compete in the World Driving Championship. Every race for the World Championship is a grand prix and F-1 cars compete in those races, but not every grand prix is a world championship race.
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Indy cars are on ovals and American based while Formula One uses proper tracks and is international.