Final answer:
A critically damped system quickly returns to equilibrium without oscillation, whereas an over-damped system does so more slowly. Both simple harmonic motion and under-damped systems oscillate, but only the latter involves damping forces.
Step-by-step explanation:
One difference between a critically damped system and an over-damped system is that a critically damped system returns to equilibrium as fast as possible without any oscillations, while an over-damped system moves more slowly towards equilibrium and does not oscillate either. Comparing simple harmonic motion and an under-damped system, a similarity is that both involve oscillations around an equilibrium position; however, in simple harmonic motion, there is no damping force present, which allows for perpetual oscillations if no other non-conservative forces are present.