[vark90]

You are right that uncertainty is a kinda loosely defined term. Usually people mean that it's a kind of proxy to the probability that the output of the model is correct in some sense.

It's also true that uncertainty can be decomposed into "flavours". The simplest and most discussed decomposition is into aleatoric and epistemic kinds of uncertainty. Epistemic uncertainty (or model-based uncertainty) usually refers to the case, when poor output is a result of the model being presented with the kind of input which it never saw before, and should not be expected to handle correctly. Aleatoric uncertainty on the other hand is thought to be intrinsic to the data itself, think of the natural ambiguity of the task, or noisy labelling.

People in the field of uncertainty estimation are very much concerned with developing methods of quantifying these different types of uncertainty, and different methods can be more sensitive to one or the other.