Learn English – it called when something is described by what it isn’t

The short answer is No, someone can’t clear up your confusion. Scholars of Greek philosophy and of dramatic criticism have been arguing about this since at least the middle of the 18th century and have come to no firm conclusion.

The slightly longer answer is that the term derives from Aristotle’s Poetics, in his definition of tragedy as

“an imitation of an action that is serious, complete, and of a certain magnitude; in language embellished with each kind of artistic ornament, the several kinds being found in separate parts of the play; in the form of action, not of narrative; through pity and fear effecting the proper catharsis of these emotions.

And that’s all he says about catharsis.

Aristotle uses the term in other works in the medical sense of purgation — so the metaphor here implies that somehow somebody is being purged of “unhealthy” pity and fear. And it’s generally conceded that he’s confronting Plato’s very negative opinion of mimetic poetry as an exciter of ‘base’ emotions and impulses —

lust and anger and all the other affections [...] desire and pain and pleasure, which are held to be inseparable from every action —in all of them poetry feeds and waters the passions instead of drying them up; she lets them rule, although they ought to be controlled, if mankind are ever to increase in happiness and virtue.

So Aristotle is presumably claiming that tragedy arouses pity and fear in order to ‘purge’ them and restore emotional balance to the hearers. But the mechanics of this operation are entirely conjectural.

There's a respectable article on Wikipedia which can usefully launch you into a deeper dive.

EDIT:
By the way, the notion of catharsis operating on characters is not widely held; and the notion of a cathartic speech in drama — basically employing the psychological sense which Kristina Lopez’ answer advances — is absent from Aristotle and from LitCrit discourse.

The basic difference between the two is emotions it appeals to.

Fun is enjoyable. It causes pleasure - especially in active forms, as thrill, exhilaration, challenge, elation.

Interesting appeals to curiosity - learning, it's about things we want to know, see, learn, examine. Whatever reasons - be it for pleasure, or e.g. for professional interest or satisfying anxiety.

Since usually satisfying curiosity is pleasurable, these two are often correlated, but not always. A gruesome sight, say, bowels sticking out of a live person's ruptured abdomen, may be interesting, but definitely not fun. A secret document on enemy military movements will be interesting too, but definitely not fun. The pilot of a damaged airplane will definitely find the damage report interesting and absolutely not fun.

On the other hand, if you solved a hundred crosswords, solving one more may still be fun, but hardly interesting. Riding down a slide in entertainment park will be described as fun too - it may be interesting the first time, but then you're not curious about it any more, you just do it for fun. Being given unexpected presents is fun - but since you didn't expect them, you didn't have time to find that interesting.