There is a big difference between assumptions and beliefs, even as the two are mutually dependent on one another. I would like to caution that it is probably unwise to conflate the two. One acts upon the other. In that way we can see that they are not one and the same.
Belief is, technically speaking, holding a proposition to be true (this is the dictionary definition). In other words, one makes an a priori assumption in the veracity of a belief (without actually knowing whether it is true or not).
So beliefs require this basic a priori assumption to even get off the ground.
But aside from this, the assumption the belief relies upon is provisional. Meaning, that the assumption will either be ratified at a later date, when there is convincing evidence to confirm or disconfirm the assumption, thereby making it true or false, or it won’t.
All beliefs are provisional for the very reason they rely on provisional assumptions.
[Note: Something to keep in mind is that people often make the mistake of thinking that their beliefs are dependent on the facts. The veracity of the belief is, but the acceptance of the belief is not.]
Faith, is different from belief as well, in that, faith makes the same a priori assumption that a belief proposition is true–but where faith differs drastically is that faith relies on conviction rather than proof (this is the dictionary meaning).
So when I speak of matters of faith–I usually mean convictions, or conviction held beliefs, or degrees of confidence in an assumption. When I speak of beliefs, I usually mean propositions which can be tested.
Hopefully this clarification helps people avoid this all too common confusion of mixing the three up.