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One has six letters and the other five. Belief is the state of mind in which a person thinks something to be the case with or without there being empirical evidence to prove that something is the case with factual certainty. Faith: firm belief in something for which there is no proof
I cheated. I use the terms interchangeably. Reckless, I know, but I'm prone to behavioral extremes.

words mean things....except when they don't