The truth is, both mean the same thing: plaster cast (
gypsum). "Gips" is the german word for "Gypsum", while "Gibs (ギブス)" is just a japanese pronounciation/writing
error of that same word. At least it's what it says on the japanese wikipedia
here. So while it would be
more correct to romanize Ringo's possibly intentional use of that error as "Gibs", the fact is... it's still an error.
As another source, there's a Shiota Akihito movie called "Gips (ギプス)" and the story revolves around a woman with her leg in plaster. So it seems that really is the most correct spelling (gi-pu-su).