The thing is that we have a basic representation, a mathematical one of various phenomena.
In quantum physics we have Shroedinger’s eq., which describes the probability of an outcome through a distribution of results. We, have to construct the Hamiltonian to describe the system. It is this description which constitutes the model.
We do similarly in classical mechanics. We identify the elements that are represented in the mathematical formalism.
In electromagnetism (EM) we again do the same. We use Maxwell’s equations, which provide a mathematical representation. The equations assist us with organizing the information available and required, to understand the system at hand.
In all cases, we have the real thing, which is measurable–many aspects of it. Thus, we reproduce those measurables and compare them, one to one, to the real thing.