Mature version just doesn't have the adult scenes, and some dialogue options related to the adult stuff won't be avaliable.
The mentions of nudity, violence are still there and the version name has "C" instead of "U".
(Honestly, it is really only there to show up on the frontpage of itch cause nsfw stuff is just always hidden.)
That's about it, the rest is the same. Even saves are compatible with each other.
Since everything but the adult scenes was already not explicit, that doesn't require any changes.