They are both examples of beliefs. Where they differ is in their claims for the justification of those beliefs. An axiom has a priori justification, claiming that it is knowable without appeal to experience. There is an assumption that experience is irrelevant to such a belief because the belief is about a necessary truth that is transcendent to experience--true in all instances. Your other example is an a posteriori belief, that is formed only through experience because it is a contingent rather than a necessary truth. It could be true or not true depending on the circumstances and can only be learned and confirmed through observation. So, we have two types of truths (necessary and contingent), learned in two different ways (reason or observation), and thus have different means of justification, but they are both beliefs held by people with varying degrees of certitude and attached values.