Counterfactual has two senses?

Hi, dear teachers.

I've just looked up the word "counterfactual" in dictionaries and found it has two meanings:
1) refer to what is contrary to the facts of an event, situation, etc.

2) refer to events that did not happen

If I understand correctly, all (implied) third conditionals express counterfactuality. But some of them express both sense 1) and 2) while some others express just sense 2).

For example,

a) His mouth would have given despair to even the drollest of fools; it was a mouth made for frowns and scowls and sharply worded commands, ...

Sense 1) is not the intended meaning of a). Instead, a) expresses just sense2).

Is my thinking right?

Thank you.