The past history of Nick Fury of Earth-77105 mirrors that of his Earth-616 counterpart until Captain America and Bucky's final battle with Baron Zemo during World War II. In this reality, Cap and Bucky would survive the attack and continue fighting during the war.
Nick Fury and the Howling Commandos were aided in the final battle against the Nazis by Captain America and Bucky. During the battle, Fury was injured, losing an eye but was saved by Captain America from being mortally wounded. Over a decade later in the 1950s, Fury was killed during the Korean Conflict, as he hadn't seen a grenade thrown from the side of his bad eye.
Because Nick Fury died during the war, he would never be selected to be the director of SHIELD.