A theory may justify ones belief. You believe in something, at some point there is justification, so without further preponderance, you approach the bounds of the belief theoretically.
On the other hand, there are the 'scientists' that go the other way around. Theories and preponderance comes first, then the belief in something tangible.
In summary, I think the most logical difference is something tangible (theory) vs. intangible (belief) given certain parameters.
A belief will follow 'supernatural' laws, a theory will follow 'natural' laws - on the other hand the end result may just be the opposite.