Rav Ashi explains that a karpaf is not a karmelis. If so, what is it? It is a reshus hayachid מדאורייתא with an issur of טלטול ד’ אמות. This begs the obvious question – doesn’t this mean that karpaf is not one of the 4 רשויות and it would be more correct to list 5 reshuyos in the beraysa on 6a, since its dinim are different than a karmelis (you are chayav mideoraisa if you transfer from רשות הרבים to it unlike the karmelis). The Rishonim address this question on 6a. Ramban answers that the beraysa is listing four different types of areas, not halachically, just physically. Their halachos are מדאורייתא only 3 but מדרבנן four. Therefore, the karpaf is not separate since physically it is a reshus hayachid. Tosfos’s (and others) answer is that the karpaf is a reshus hayachid gamur and only has the din of karmelis for carrying 4 amos within, so it is not new – it is like two reshuyos already counted, in some aspects like reshus hayachid and some like karmelis. The footnotes in the Ran explains this difficult answer that the gezeira of carrying in a karpaf does not define the area differently (as chazal did by karmelis), it just creates an איסור גברא, therefore it is not counted.
(Interestingly, see yerushalmi that says:ארבע רשויות לשבת: רשות היחיד, רשות הרבים, וכרמלית, ומבואות שאינם מפולשין )