Piggy back & Aftermarket ECUs:

Piggy back ECUs connect between your existing ECU and the engine sensor inputs and outputs. All work slightly differently and apply some or all of the following combinations.

Some will adjust the sensor readings such as air temp, engine speed, crank position and effectively lie to the standard ECU forcing a more aggressive timing. Some will actually perform their own calculations and take over control of some aspects of engine management like turbo waste gate control and ignition timing.

Some will take the standard ECU output and modify the signals sent to change timing and learn to guess the next output a split second before it is needed using the base ECU map and just enhancing it a little.

Tuning boxes are relatively new and these alter readings going to and from the ECU giving extra power or economy.

Aftermarket ECUs are often direct replacements for the car's ECU and will take over all the functions associated with it. They are generally faster and able to cope with a wide variety of additional factors such as water/methanol injection and a turbo timer.

Be wary though, as some piggy back ECUs and aftermarket ECUs do not include knock protection. If this is the case then set your timing conservatively and use high octane fuel.