Bakufu was originally a concept which referred to a shogun's camp and when MINAMOTO no Yoritomo was appointed to Ukone no daisho, his house, the Okura palace, was called bakufu, but it was not a word for Kamakura bakufu as a samurai government established by Yoritomo, but a word for the private house.
幕府とは、そもそも将軍の陣所を指す概念であり、源頼朝が右近衛大将に任官したことで、その居館　大倉御所を幕府と称されたことがあるが、それは私邸を指す言葉であり頼朝の開いた武家政権としての鎌倉幕府を指す概念ではなかった。