The difference between theories and models is a theory, in general terms and based upon a hypothesis or idea, is testable. It is confirmed by a repeated observation or experiment. However, theory is applied to many aspects such as psychological, scientific or medical field. Models, on the other hand, are used to represent and input information and results.
Why is it important? Because, for example, the field I teach in, human relations and psychology, we often use models to explain a theory like human interaction, the Johari Window is a model that can be used to explain human action and its process. This model was developed by Joseph Luft and Harry Ingham.
Although theory and model are different in meaning, they are counterparts with each other in psychological, scientific or medical field. I have posted some websites below for your further research or interest.