I would however, reverse your two definitions, I think the word belief suggests the more rational, evidence based mental model, faith is a subset belief that requires no evidence.
All of us have beliefs (under my schema above) that are evidence based (we believe in the atomic model). Often our beliefs are all tagged with a mental estimate of their surety, based on perception of the evidence and the criticality of the belief, the side effects of it being wrong. Items whose falsehood is not critical can be believed with much less evidence than items whose falsehood is critical. I may believe that Walmart has the best price on a coffeepot, and that is enough to commit a few dollars to the purchase, knowing I could be wrong but that it is not consequential. That same level of belief may not be adequate to purchase a Walmart parachute. It's one thing to believe a newspaper story that a man has the legal name of 'Santa Claus', and a very different to believe he drives flying sleigh & reindeer, or that some 1000000 people wandered in a desert for 40 years WITHOUT A TRACE of evidence, while Egyptian military encampments (only a few dozen men) in that same area and historic timeframe) have been well documented. The key distinction between rationality and religious faith is that scientific, historical and other rational theories (beliefs) are known to be subject to revision, and are constantly evaluated in that framework. Religious faith, however, is not tied to evidence (sometimes searching for evidence is actively discouraged) and is considered true, not really subject to revision. This is, I guess not surprising. A system that in principle takes over one's entire life would have problems if the subjects realized that what is 'right' today might not be right tomorrow. So skepticism is portrayed as evil, critical thinking discouraged and the truthset declared absolute to protect its stability and belief without evidence (faith) is represented as the highest pinnacle of thought. Protecting tat faith becomes more important than reaching quantifiable truths. jay