For questions generally related to various automobile racing sports. For questions specifically related to Formula 1 and NASCAR, see the "formula-1" and "nascar" tags respectively.
Automobile racing, auto racing for short, is a broad class of motor sports in which land-based, primarily 4-wheeled vehicles and their drivers compete in tests of speed, distance and/or precision.
Leagues exist for virtually every practical combination of vehicle, terrain and race format. Some of the most popular forms of auto racing include:
Formula One - Governed by the Italian-based FIA, this class of open-wheel, open-cockpit racing is presented as the premiere test of driving skill and mechanical prowess. The cars are close to if not the most powerful in terms of engine displacement and power, and the drivers are among the best in the world, many of them having earned a spot with a Formula 1 team by demonstrating prowess in other road course leagues including Indy Cars, GT and lower Formula leagues.
NASCAR - The National Association of Stock Car Auto Racing is the administrative body behind the Sprint Cup Series, the most popular motor racing league in the United States by spectator audience. The Sprint Cup Series uses closed-wheel cars superficially similar to production full-size sedans and coupes from U.S. factories, but contrary to the term "stock car" the national divisions of the sport have not used factory-built cars for some time. The NASCAR governing body oversees several regional-level competitions that do feature production automobiles with limited modifications allowed.
GT - Short for "Gran Turismo" (Grand Touring), this racing class grew out of European upper-class traditions of young men taking a "grand tour" of the continent by car, requiring them to negotiate traditionally narrow, winding European roadways. The genre of luxury sports cars designed to be exceptionally well-suited to this task, from such well-recognized names as Mercedes-Benz, BMW, Ferrari, Lamborghini, Porsche, Aston-Martin, Jaguar etc eventually began to be pitted against each other in races modeled after the Grand Touring routes. This evolved into what is now known as GT racing, which is governed by several regional and international bodies but centers around road courses driven by competitors in various makes of sports car based on production models available to the public, with varying amounts of modification allowed depending on class.
Le Mans - Derived from a historic 24-hour endurance race for both driver and vehicle, this style of time-based racing encompasses several classes of vehicle, from production-derived "GT" classes up to "prototype" designs that must be closed-wheel, but are otherwise not dissimilar to Formula 1 chassis. Very often, multiple classes of car share the track for the same timed event, and compete for each other tactically for track position while driving but are only compared to others of the same class to determine race and league standing.
Indy Car - An American derivation of the Formula-style open-wheel racing, this class of open-wheel, open-cockpit racing, currently governed by the Indy Racing League, rivals Formula 1 in top speeds. Indy Car races are held on a variety of tracks, from sections of city streets to dedicated road courses to simple oval tracks. Currently the popularity of this series is on the decline in favor of NASCAR which has events on many of the same tracks, though as the cars are open-wheeled, the skill required to gain and maintain position on the track is much higher as even minor contact between cars can cause damage and/or a loss of control.
Desert Racing - This style, with the premiere Baja 1000 event governed by SCORE International, features a wide array of customized vehicles designed for high speed over uneven off-road terrain. The vehicles compete in a series of distance races, often in mid-summer in the American Southwestern/Northern Mexican deserts, making the event grueling for both driver and vehicle. Similar vehicles are also seen in arena races on artificial dirt courses, as well as winter courses carved out of snow.
Drag Racing - This style of racing emphasizes straight-line acceleration along a set distance (often a quarter-mile). This is one of the more popular and accessible forms of racing to average auto enthusiasts, and events range from illegal street races held on deserted rural roads with modified "muscle cars" up to NHRA-sanctioned events using custom-built "funnycars" and "top fuel dragsters" on purpose-built drag strips.
Rally Racing - This is a form of racing nominally compatible with ordinary road traffic, in which teams of drivers in production-derived cars compete to hit a series of checkpoints along a route at specific times from their start time. Deviations from the prescribed checkpoint time, either too early or too late, score penalty points. Races are typically held in "stages", often punctuated by the most popular type of rally event known as a "zero time" or "time trial" stage in which the "checkpoint time" is zero seconds, and therefore the objective for the drivers is to complete the stage as quickly as possible. Various styles of time trial stage include downhill and uphill climbs (often combined into a single event where the car has to get up a hill, turn around and come back down) as well as paved and dirt variants of traditional road tracks.
Drift racing - This is a showy style of racing in which the cars, similar to GT or Rally production-based models, are equipped with slick, hard-compound tires that slip sideways easily. The cars therefore oversteer more easily, and the drivers in fact maintain a controllable amount of oversteer and even "four-wheel drift" as they negotiate turns. Drift races also typically feature very narrow tracks with tight turns requiring precise control of speed and throttle from the approach through the exit of each turn. The skill required rivals that of open-wheel racing, though the speeds, owing to the lower traction, are much less and therefore the sport tends to be safer for drivers and spectators in the event of a crash.