The difference between epistemic and aleatory uncertainty is not well understood even in the machine learning world. Most applications of machine learning to domains where uncertainty needs to be quantified use aleatory uncertainty, when epistemic uncertainty is the right one. I wish we had better ways to explain these concepts, and perhaps better terms too. Alternatives like intrinsic/extrinsic or irreducible/reducible don't really work either, because they make it seem like it's a dichotomy.