# When is a dynamical system discrete vs. continuous?

I have a basic question to ask:

Let's say I am reading a paper which gives a good model that consists of a set of ordinary differential equations, with first and second derivatives. Continuity is a requirement for differentiability, as we learned in an Analysis course.

Now, I simulate this model, writing code in Matlab, and calling a basic ode solver, ode45, which is a version of Euler's formula but with adaptive time-stepping. Then, the equations are being solved with a discrete method, namely, with discrete time-steps. There are no exact solution formulas being solved for.

Then, is this a discrete or continuous dynamical system?