I don't know anything Airbus specific but generally speaking groundspeed displayed on MFDs (and some PFDs such as 777) is calculated by the navigation system utilizing both heading information as well as TAS information generated by the ADC (or whatever your flavor name for ADC is, be it ADIRU, ADIRS etc).
To solve for TAS, you need a good measurement of either TAT or OAT. In transport category jets these days TAT is what's used by means of the TAT probe in concert with the data generated by the static and pitot ports.
Usually TAT isn't very reliable on the ground and def not until it's heated up by some real friction and not by the metal just sitting there being either cold by the outside temperature or being heated by the sun in warm places because of its metallic color.
I believe and I could be entirely off base here, that because the TAT isn't reliable on the ground and at very low airspeeds that some of the data generated by its mean is suppressed purposefully because of that. Wind drift/velocity would be a good example of that.
Now if you ask why do they still display TAS next to GS showing them equal... I have no idea. One would think they'd suppress that too but I know some airplanes display that along with SAT which is obviously wrong too since it's a derived calculation based on TAT.
In particular as an answer to your drift question. It's based on heading course and TAS. Usually provided to you seamlessly by the FMC or whatever is doing the navigation portion of your overall system/fabric that is in the end displayed to you as one picture on both MFD+PFD.