In racing terms, "formula" implies a pure racing car, a single-seater with open wheels — a format largely unconnected with, and unrecognisable from, road cars. Formula One implies that this is the ultimate in formula racing.
"Formula" One and the baby formulas that came later
The reason why the sport is called "Formula" One is rooted in history. Pioneer motor racing placed no limitations on the size or power of the competing cars. With technological advances, this free-for-all quickly made for ludicrously dangerous conditions — especially as the early races were fought out on public roads. As a result, the governing body of the sport at the time began imposing key limitations on the format of the cars in terms of power, weight, and size. Only cars complying with this "formula" of rules could compete. The rules of Grand Prix racing have adapted to the technology and needs of the times. The rules formulated for racing immediately after World War II were given the tag of "Formula One", a name that has stuck ever since. Formula Two was invented shortly afterwards as a junior category, with a smaller engine capacity. Not long after that, Formula Three came into being for even smaller single-seaters. The Formula Two name was dropped in the mid-1980s and replaced by Formula 3000, denoting the cubic centimeter capacity of the engines. Formula Three remains. If illogical and inconsistent labelling bugs you, motor racing is not for you.
The premiere racing sport in the world
Formula One stands at the technological pinnacle of all motorsport. It's also the richest, most intense, most difficult, most political, and most international racing championship in the world. Most of the world's best drivers are either there or aspire to be there, and the same goes for the best designers, engineers, engine builders, and so on. It's a sport that takes no prisoners: Under-achievers are spat out with ruthless lack of ceremony. Formula One takes its position at the top of the motorsport tree very seriously.
Formula One traces its lineage directly back to the very beginnings of motor racing itself, at the end of the nineteenth century, when public roads were the venues. All other racing series have sprung up in its wake.
Unlike most racing categories, Formula One isn't just about competition between the drivers. It's about rivalry between the cars, too. The technology battle between teams is always an ongoing part of Formula One.
Comparing Formula One and other types of racing
Racing in America for a time overlapped in its development with European racing; then it veered off in the direction of oval track racing.
CART and IRL racing in America
Formula racing in America became Indy Car racing, spawning the CART and IRL series of today. These cars look like Formula One cars to a casual onlooker, but a Formula One car is lighter, more agile, and more powerful. Another difference is that Formula One cars never race on ovals; instead they race on purpose-built road racing tracks or street circuits. Furthermore, each Formula One team designs and builds its own cars rather than buy them off the shelf from a specialist producer.
NASCAR and Touring Car racing
Non-formula, road car-based racing spawned NASCAR in America and Touring Car racing in the rest of the world. Both are for cars that from the outside look like showroom road-going models but which underneath the skin are very different. NASCAR tailors to American production models and races mainly — though not exclusively — on ovals. Touring cars are based on European or Australian road cars and, like F1 cars, race on road racing or street tracks.
The feeder formulas
In Europe, feeder formulas to Formula One — where drivers, team owners, designers, and engineers can all hone their craft on the way to Formula One — developed. Today these are classed as Formula 3000 and Formula 3. The names and numbers have changed over the years, but Formula One remains what it has always been — the pinnacle. F3 is currently for single-seater cars with engines based on road-going production cars not exceeding 2-liter capacity. F3000 is for single seaters powered by a specific 3-liter racing engine defined by the governing body.
The structure and hierarchy of motor racing is extremely complex and not very logical. All you really need to know is that, in global terms, Formula One is at the top of the pyramid.