WHAT IS A THEORY
A theory is a set of statements that are arrived through a process of continuing abstractions. A theory is aimed at a generalized statement aimed at explaining a phenomenon. as opposed to traditional or conventionalists views (which also share a shared view with platonic philosophy which aimed at elemental truths) that are detached from the mundane physical state of nature more recent (Popperian View) says that theories are falsifiable through experimentation.
The second difference is also the abstract nature of the theory as opposed to more ‘realistic’ nature of mathematical modeling. A third difference is that in mathematical modeling the approximation is usually based on experimentation while theory does not necessarily need experimental support for its postulation.
A model is a purposeful representation of reality. In general when people refer to modeling, they refer to mathematical modeling which is a mathematical construct that is an approximation that is used to study a specific phenomena.