Drivetrains are the arrangement of the engine and drive wheels in relation to each other. Four wheel drive, front wheel drive, and rear wheel drive are the three types of wheel layouts on four wheeled vehicles. Engines can be mounted in the front, middle, or rear, and any of these layouts are able to handle any of the three drive wheel layouts.
Front-wheel drive has become fairly standard in today's economy cars, and some more affordable sports cars are produced with this layout. It isn't favored for racing situations because it puts a lot of stress on the front wheels and very little on the rear wheels. A benefit to this layout is that the driveshaft is eliminated, and drive components can be built together, reducing weight and cost.
Many American sports and muscle cars have this layout, and is favored by many racing car drivers/teams for its handling characteristics. It is considered by some the optimal road/track layout because the front wheels only steer while the rear wheels drive the vehicle forward.
Four-wheel drive is a layout where power goes to every wheel. This is favored in low-traction situations like off-roading, where the front or rear wheels may lose all traction. It is also more difficult to spin the wheels faster than the vehicle is going (sometimes called a burnout) because the engine would have to spin all four wheels, and the torque per wheel is half that of a two wheel drive vehicle. The disadvantages to four-wheel drive is that it requires two differentials, which adds more weight to the vehicle, and the front wheels spin faster around a corner, so a center differential is required to prevent slipping on high grip/paved surfaces.
This is the standard layout for economy and sports cars alike. It is as common as it is because of a combonation of history, familiarity, and construction ease. The engine sits in front of the driver and passengers, and is usually really close to the front axel location. These cars are often front-heavy, and more dependent on power steering.
Exotic cars and high performance racing cars are often found with this layout due to its favorable weight balance. The engine is between the front and rear axels, behind the driver and passenger(s). Some consider a car to be either front-engine or rear-engine based on where it is in relation to the seating.
This layout is banned in some forms of motorsports, while in others it is the only competitive layout in the series. Because there is no engine under the hood, the space is often used as a trunk.
Some consider most mid-engine cars to be rear-engine cars, but true rear-engine cars have the engine mounted behind the rear axel. Many early versions of this layout were difficult to control.
Front-Engine, Rear Transmission Layout
This layout is rare, but it was designed to distribute weight more evenly. The transmission on any car is usually mounted right to the engine, but this layout has a transmission mounted to the differential. Part of the weight that would be in the front is now in the back. This layout is limited to rear-wheel drive.
Other Drivetrain Layouts
In the early days of the automobile, before the differential was invented, many vehicles were one-wheel drive.
In hybrid cars, it is possible for one engine to drive the front wheels, and the other engine to drive the rear wheels. So far no examples of this design have gone into mass production, but some concept cars have featured this design.