In my experience it's a third option - that optimistic and pessimistic people have different experiences and evidence.
So when people say they are an optimist, they mean "in general the evidence that I have leads me to a more positive conclusion than most people"
I would say that's a special case of my second option. Maybe I didn't phrase it broadly enough. It concerns a single question or issue. (Unless somebody thinks they have some magical evidence or experience that concerns literally every issue, which I would find highly suspect).
If people in such situations care about their conclusions (which may not always be the case, not all issues are equally important), they would proceed to share the evidence and experiences.