Discrete event simulation is appropriate for systems whose state is discrete and changes at particular time point and then remains in that state for some time. An example of such a system is the number of customers in a post office: The number of customers is discrete (integer) and the number of customers only changes when someone enters the post office or finishes its business at the counter.

Continuous simulation is appropriate for systems with a continuous state that changes continuously over time. An example of such a systems is the amount of liquid in a tank and or its temperature. Such a system can be described by differential equations. Continuous simulation is a technique to solve these equations numerically.