Ehh, I'm not convinced the vocabulary there fits. An error can be an exception, if it was unexpected. That's the real distinction: errors are expected and can (optionally) be handled explicitly. Anything unexpected, in your code or within a library function, is an exception and should bubble up / halt execution. But the trouble is that _expectedness_ isn't often a language construct, but more like business logic, and will have different meanings (and presumed severity) between library author and end user.

I think there are a lot of schools of thought on this precisely because it is a difficult problem to solve: it requires getting a bunch of programmers to agree about how the edge cases should be handled, and that's no small feat.