Isn't the whole point of a space telescope so that you don't need adaptive optics? Or are you making a joke?

You need compensation against seeing for very, very big space telescopes, the kind that can resolve a moon in orbit of an expoplanet. IIRC there are reasons against using adaptive optics there, so you might need speckle interferometry there.

I am merely interested in the subject, but from what I understand, there are different types of adaptive optics.

I am specifically curious about the kinds to allow for seeing exoplanets by blocking the light of their star.

A lot of people don't know that adaptive optics is meant for atmospheric usage only.