What is the difference between difference equation and differential equation?

A difference equation relates the values of a sequence at discrete points, typically involving shifts in the sequence, such as (y(n) = ay(n-1) + b). In contrast, a differential equation involves continuous functions and their derivatives, describing how a function changes over continuous intervals, such as (\frac{dy}{dt} = ky). Essentially, difference equations are used for discrete systems, while differential equations apply to continuous systems.