Am I wrong to say that even if the universe of your concern is discrete, calculus can at least describe the behavior of recursive discrete processes, among other things?
Depends on the process and the exact form of the discreteness.
Discreteness introduces discontinuities and errors, and it's usually possible to describe the errors analytically. But there are situations where discrete systems become numerically unstable and blow up while the smooth analytic equivalent has no problems.
Discreteness introduces discontinuities and errors, and it's usually possible to describe the errors analytically. But there are situations where discrete systems become numerically unstable and blow up while the smooth analytic equivalent has no problems.