This really does depend on the field you are asking about and even on the individual you are talking to. For example, one economic text that I teach out of explicitly says that a theory and a model are the same thing and that the words can, as you say, be used interchangeably. In other books, however, the words are used differently.
When they are used differently, the difference is usually that a theory is more abstract and generalized while a model tries to actually predict something more concretely. A theory tries to explain things while a model tries simply to put the theory into action.
So, for example, you could have a sociological theory that argues that there is a connection between broken windows in a neighborhood and crime. This theory would explain the causal connection between the two. It would say that broken windows lead to a feeling that no one cares about the area which then leads to a feeling that anything goes and crime is okay. But a model would be more specific. If might try to actually predict a numerical relation between the number of broken windows in a given area and the number of crimes. It takes the theory and tries to make it more predictive.
This is one way to differentiate between a theory and a model, but you should be aware that not everyone has the same understanding of these terms.