I always thought that 'engine management' concerned the 'engine', exhaust and their electronic devices to make it function sweetly and not the gearbox, rear axle, etc. But I might be living in the Dark Ages. One would think that the battery was disconnected for the earlier investigations and a reboot wouldn't be necessary, but who knows?
It's often referred to as the Power-train Control Module that generally monitors the cars systems and I also feel that I belong in the dark.
If I can quote from Wiki:
A power-train control module (PCM) is generally a combined control unit, consisting of the engine control unit (ECU) and the transmission control unit (TCU). On some cars there are multiple computers: the PCM, the Transmission Control Unit, and the Body Control Module, for a total of three separate computers as an example.
The PCM commonly controls more than 100 factors in a car or truck. There are many hundreds of error codes that can occur, which indicates that some subsection of the car is experiencing a problem. When one of these errors occurs, usually it will turn on the "check engine" light on the dashboard.
Engine Control Unit (ECU) is also called:
PCM: Power-train control module (Ford/GM)
ECM: Engine control module
Injection control unit (Peugeot, Citroen, Fiat, Alfa, Lancia)
DME/DDE: Digital Motor Electronics / Digital Diesel Electronics (BMW, Mini)
ECU: Electronic control unit
Loooooong way away from lifting the bonnet, checking the ignition timing, turning the mixture screw on the carb and getting it running right.