The Drivetrain of a car is a term which describes the engine setup or location and the means by which the engines power is directed to the road. This is usually made up of a abbreviation of the engine location and to which wheels the power is delivered.
FF
FF describes a vehicle which is front-engined and front-wheel driven. Front-engined simply means that the engine is located ahead of the driver. This setup is very common in popular, low-powered road cars, such as the Ford Focus ST '06 or Toyota Yaris RS 1.5 (J) '00. The FF setup is generally regarded as good in low grip scenarios (though not as good as 4WD), but subject to understeer in normal conditions due to the steering wheels also delivering the power. High performance vehicles rarely use the FF layout because weight is transferred to the rear wheels under acceleration, while unloading the front wheels and sharply reducing their grip. An FF drivetrain vehicle is required for entry into the FF Challenge events in Gran Turismo.
FR
FR describes a vehicle which is front-engined and rear-wheel driven. This setup is used for most modern cars since it provides good controlled power, while leaving the front-wheels to steer the vehicle. During acceleration, weight is transferred to the rear wheels, which improves the efficiency of the driven wheels. Under braking however, the weight shifts to the front wheels, which aids in steering around corners. Many high-powered sports cars feature a FR layout, such as the Mazda RX-7 GT-X (FC) '90 and Honda S2000 '01. An FR drivetrain vehicle is required to enter the FR Challenge in Gran Turismo.
MR
MR describes a car that has its engine in the middle of the car and that is rear wheel drive. Since the weight is balanced, there is not as much of an oversteer problem as FR cars. Thus, it is prime for racing because the rear wheel drive saves weight. Examples include the Acura NSX '91.
Cars of this drivetrain are required to enter the MR Challenge.
4WD
4WD denotes that a vehicle sports a Four-Wheel Drive system. While this can be supported by any engine location, it is usually paired with a mid-engined setup in sports cars or a front-engined layout in off-road vehicles. The four-wheel drive setup is advantageous in that it improves control and torque. It is usually used in off-road or rallying cars, such as the Lancia DELTA HF Integrale Rally Car '92, or high-end supercars such as the Lamborghini Murcielago LP640 '09, though there are some that defy this trend, such as the Peugeot 205 Turbo 16 '85 (being a WRC homologation model with a mid-engine setup), the Audi A3 3.2 quattro '03 (being a family car with a front-engine setup), or the RUF CTR2 '96 (with a rear-engine setup).
A 4WD layout is required for entry into the 4WD Challenge in Gran Turismo.
RR
RR refers to a vehicle that features rear-wheel drive paired with an engine located behind the rear axle. While this is good for acceleration, this setup does not provide good grip in high speed corners and can lead to uncontrollable oversteer under braking. Not many examples of this exist in the Gran Turismo universe and there is no event strictly for the RR drivetrain. The original Fiat 500 and derivatives of the Porsche 911 such as the RUF CTR "Yellow Bird" '87 are examples of this.
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-- means that the drivetrain is unknown. Technically it is not a drivetrain, but is presented as one in the games. Examples include Chevrolet Chaparral 2X Vision Gran Turismo. As it is not a real "drivetrain", there is no category for it.