This study compares the behavior of differential equations and difference equations of various orders in order to predict the state of the systems at a given time by using initial information about the system. We have demonstrated that differential equations are used in a continuous domain whereas difference equations are employed for discrete dynamical systems. Furthermore, the difference between the two models is amplified in logistic models which both are known to give explicit solutions. However, the discrete logistic model is especially superior in exhibiting a chaotic behavior of the system which the differential equation is incapable of dealing with. The conclusions drawn from the findings conform the similarities and the stark differences between these two models.