I've never encountered with "improvisional theater". How does it work? What practically is "performing without a script"? You stay on stage and say anything that comes to your mind?
Improv can take a lot of forms -- there's one style that's basically "make up a movie, complete with narrated camera moves". There's another that's "a series of unconnected scenes". My team is doing one now that is basically an improvised podcast or radio play.
Simply "standing on stage and talking" is bad form, because it's not especially interesting. How many tv shows are just people talking? None; people are doing _something_. Sometimes those people are very active, like if they're riding a dragon into combat. Sometimes those people are less active, like if they're a radio host talking to callers. But never are people just standing: they're adjusting the radio microphone, or flipping a page to read off of.
So, role playing games?
There's definitely overlap!