In a "common ground" dual transformer system the commons (or "ground") for the heating and cooling transformers must be connected to each other and supplied to the thermostat through a single connection at the "C" terminal. In this arrangement, it is very important to keep the Rc and Rh (power from the cooling and heating transformers) separated and the thermostat must be designed and installed to handle separate heating and cooling power supplies. If the commons for the two transformers are not connected, then a single thermostat will not be able to control both the heating and the cooling units unless you install separate control relays that are all actuated by either the heating transformer or cooling transformer along with the thermostat (typically the heating transformer is used as the power supply in this case). If the two transformer commons are isolated in this arrangement then, yes, each common for the cooling and heating are only for the cooling and heating units, respectively. This could not be called a "common ground" system, however.
As a general rule, provided the heating transformer has a sufficiently large VA rating, I would recommend disconnecting the separate cooling transformer and instead power all the controls from the heating transformer only to reduce the possibility that someone will accidentally use an incompatible thermostat or cross separate Rc and Rh supplies in the future.