One of the most common reasons for such a process is related to the numericali ntegration of ODEs, but there is no unique way of doing this.
The simplest method is to use that approximation:
So defining $\Delta_h f(x)=f(x+h)-f(x)=hf'(x)$.
But these are approximations of a continuous process by discrete.
As I said before we need more context.
We want to convert the ODE $y''=-y$ into a difference equation. I will use repeated approximation by a difference quotient:
with initial conditions $y(0)=0,\ y(h)=h+y(0)=h$
and the rest is algebra