Dear Amer,
If I understand your question correctly, you may be talking about <E> = sum_i {E_i * P_i} and <P_i> where p_i are the populations of states (e.g. KS orbitals) and E_i are the energies of these states. The first quantity tells you how the average electronic excitation energy changes in time (e.g. due to nonadiabatic transitions). The second quantity tells you about the probabilities of finding the system in any state i as a function of time.
You may want to look at this paper: Phys. Chem. Chem. Phys. 2018 20, 25275-25294. It defines the quantities and discusses the differences in terms of relaxation timescales.
Hope this helps,
Alexey