Probabilities do not necessarily designate variability or indeterminacy in nature. Probabilities may instead represent ignorance. The former type of uncertainty may be called aleatory. (It goes by other names -- for example, chance.) The latter type of probability -- the one that represents degrees and forms of ignorance -- is often called epistemic probability or uncertainty. (This type of probability is also called different things. For example, it is sometimes called credal probability.) See Brian Weatherson, Keynes, Uncertainty and Interest Rates
The source or cause of uncertainty is important. It is important to know if our uncertainty about an event or hypothesis is attributable to the way the world works, to the chance elements in the world in which we live; or whether our uncertainty is attributable to the lack of information or our uncertainty about methods of assessing the information or evidence we have.
I have often fumbled (largely by remaining silent) in explaining the difference between my interest and the focus of people who are mainly interested in matters such as random variables and causality. The difference is that the people who are interested in the latter are generally interested in patterns of random or chance behavior in nature whereas I am more interested in incomplete evidence and inconclusive argument.
The confusion between aleatory and epistemic probability or uncertainty is perhaps partly attributable to the fact that the aleatory properties of nature often shed light on the appropriate treatment of incomplete information and on appropriate argument from and about evidence and information. In addition, it is very often the case that we have uncertainty compounded, that (some amount of) chance is wrapped in (some degree of) ignorance.