In general, the continuous model describes the solution or a function of it in all points in time and space. In practice, in particular for the large problems we want to solve, this is not feasible. Therefore we limit ourselves to compute the solution only in finite number of points, which are picket up according to some suitable rule.
Note: In some branches of engineering, the term 'discrete' is used to describe a system with periodic or constant time steps. We do not consider those cases in the current context.