I asked my dealer the same question and got the following response;
"The sport suspension is a constant suspension set up that actively varies the damping to give a more sporty feel. There is not a button to turn this on or off.
With the skyhook active damping suspension there is a button to firm up the suspension to allow for a more sporty ride or you can leave it in the standard mode for a more comfortable ride.
Sport Skyhook: electronic suspension control system
The Ghibli can be equipped with optional aluminium shock absorbers and independent dynamic electronic control. The system monitors a wide range of parameters, including vehicle dynamics (speed, lateral and longitudinal acceleration), body and wheel movements, shock absorber dynamics (compression, extension, piston speed) and, depending on the drive mode selected by the dedicated button, the system adjusts the ideal damping conditions for the current handling situation, for each wheel separately. The car's independent suspension control is one of the standout features of the Ghibli. When the car is switched on, the shock absorbers are set to give priority to comfort. By pressing the suspension button on the gear shift lever bezel the setting changes, and the shock absorbers become more rigid, thus significantly changing the car's handling. This setting, developed on the track and in extreme conditions, is characterised by reduced load transfers, both longitudinal and lateral (i.e. stiffer) and allows the car to show its sportier soul.
Sport set up option;
The option Sport set-up is visually characterized by the lowering of 10 mm of the vehicle, obtained with the use of specific springs, more rigid, and by the use of shock absorbers KONI, a variable damping self-adaptive hydraulic type, depending on the frequency of the stress. This feature allows to customize the damping according to the dynamic conditions thanks to a valve acting differently in two situations:
• Stress at low frequency, typical of the movements of pitch and roll, which require high damping.
• Stress at high frequency characteristics of the steps of obstacle and on rough roads, which require low damping.
The transition between the two operating modes, calibrated with road tests, allowed to give the car a well-defined sporty handling, without affecting the behaviour of the car on bumpy roads."
I chose to order the skyhook but do not have the car yet and have not tried either of the above options.
Hope this helps.