How might a theory relate to a model in science?

These two things are related but can be independent, because it is possible to ... of theories is studied formally in mathematical logic, especially in model theory.

A theory may be a set of statements that are developed through a method of continued abstractions. A theory is aimed toward a generalized statement aimed toward explaining a development. A model, on the opposite hand, maybe a purposeful illustration of reality. As you'll be able to see, each shares common parts in their definitions.