They both mean that the shared information will be shared with the public in just the same way any public web site is - it can be accessed by the general public.

Public sharing is a powerful way to open your information to easy access by anyone in the world. Because of this, you should be extremely hesitant to check the "edit" box when you've granted Public access - if you do, anyone in the world can edit or delete your information. Also note, that KeepandShare only allows logged in users to edit information shared with them, even if the information has the 'public' share group.

"Really Public" means that in addition to being publicly accessible your information may also receive additional exposure & promotion by KeepandShare to help drive traffic to your shares. For instance, KeepandShare might list your share in the "Cool Shares" lists to encourage people to visit.