The Formula 1 world championship is governed and owned by a world body of motor racing based in France, called the International Automobile Federation, or FIA. The commercial rights to F1 are leased by the FIA to a British man named Bernie Ecclestone. NASCAR is owned by the France family - as opposed to the country - although it too it is a private racing series.
NASCAR racing cars resemble the cars that you drive on the highway, your basic road cars. Formula 1 cars look like insects - you know, they have long snouts, wings, the wheels are entirely outside the body like an insect's legs and the drivers are visible in the middle of all this like the bug's eye.
NASCAR has the reputation, fairly or unfairly, of appealing to a bunch of yokels, whereas Formula 1, fairly or unfairly, has the reputation for appealing to intellectuals - except for the fans of the former driver, Michael Schumacher. Formula 1 fans are supposed to be motor racing purists who take pleasure in watching cars perform the perfect lap on winding circuits, while NASCAR fans are supposed to be interested in watching cars crash as they go around in circles in a tightly knit pack.
Formula 1 is to NASCAR what basketball is to soccer, like the difference in the goals in those two sports. There is very little passing on track in F1, but when a car finally does pass another the world celebrates - as with the rare goals in soccer. In NASCAR, cars pass each other all the time, like goals scored in basketball.