In a narrow sense, the Genji Shoguns are identified as three generations of Shoguns that commenced with MINAMOTO no Yoritomo (who set up the Kamakura bakufu (Japanese feudal government headed by a shogun)), MINAMOTO no Yoriie and MINAMOTO no Sanetomo.
源氏将軍とは、狭義には鎌倉幕府を開いた源頼朝、源頼家、源実朝の三代の将軍を指す。