Almost all cars up until approximately 1975 the cooling system was driven by a mechanical fan powered by the engine. After this time electrical fans were fitted to quality cars and final to all motorcars.
Both systems have their minuses and pluses. The mechanical fan remains running the entire time the engine is running and is powered by the engine by the means of a pulley. The pulley is attached to the piston shaft on the outside of the engine. Power is transmitted from the pulley to the fan by a fan belt.
The advantages of this system is the engine is being cooled the entire time the engine is running and the fan increases in speed the faster the engine goes. The disadvantages are it is only suitable for cars with in line engine. The reason being the pulley that drives a mechanical fan has to be attached to the piston shaft. Therefore the engine has to face forward for this system to work. The system can only fail if the fan belt snaps or the fan blades get damaged.
Electrical fans was introduced with the transverse (side mounted) engine. Transverse engines became very popular because they save space. This means a small car can house a powerful engine if required. It also means smaller cars can be built like the British Austin Mini of the 1960s.
Electrical fans work when the engine reaches a particular temperature. This is done with a thermostat switch which is located on the radiator. When the car has sufficiently cooled the fan will cut out. When the fan is not operational normal cooling is done through vents or the radiator grill. Some cars have more than one electrical fan. The fan is also located on the rear side of the radiator. Electrical fans are relatively trouble free. The fan only operates when the car is very hot it remains mostly idle. This means it will probably last the life of the car before the bearings wear out and the fan fails.
One is more likely to have problems with detached wires which can be disturbed when maintenance is being preformed. The other common cause of failure is the thermostat switch failing. These are cheap to replace and relatively easy to fit and in the scope of the DIY mechanic and requires the minimum of tools. Sometimes the thermostat switch is only held in place by a clip. In this case it is only a matter of replacing the thermostat pressing down the clip and reconnecting the wires.