This will be a short post, I think, but basically the question for a theory of knowledge here is: What are the criteria for believing something? In the language of philosophers, it's: "What is the epistemic justification for my belief?" (The latter, I think, sounds a lot uglier and unnecessarily verbose.) And there have been two ways, traditionally, that philosophers have approached this question. One suggestion is that saying I have a reason to believe something is equivalent to saying I'm under no obligation not to believe it, given whatever further specific criteria somebody would want to give; this view has been called deontological justification. Another possibility suggested is that saying I have a reason to believe something is equivalent to saying that I believe it because the proper processes, perhaps cognitive processes that allow me to make certain factual connections for example, result in the belief I have; this has been dubbed a non-deontological justification.
Basically, the distinction comes down to this. Either I have a reason to believe something because I'm not under obligation not to believe it or I have a reason to believe something because some correct processes or other brought about the belief. The word 'obligation' in the former part of the sentence there is what makes the belief a matter of deontology, which is related to one's duty to do something. The latter is about some kind of natural mechanism (perhaps) that results in the belief.
It seems as though both hypotheses could be true. We could believe, at least at the level of informal speech, that I have a good reason to believe something because, well, I can't think of any reason not to believe it that would count as evidence against it. And we could believe at the level of explanation related to causes and mechanisms that I believe what I do because of a certain kind of cognitive process, and when my cognitive processes have no failed me, then that makes me have beliefs with good reasons for those beliefs.
Argument to the contrary would appear to be so much argument at cross purposes. They are just two different ways of analyzing phenomena, namely in this case, belief formation and good reasoning. The world is big enough for both.