Social distance.
One could think of the conflicts where a communist/socialist side used this to send soldiers to defend the exploited proletariat from the imperialistic bourgeoisie. This can be entwine with moral distance too. However Grossman talks about something very different which can be applied to many more conflicts. This is the distance between officers and the simple soldiers and this distance helps the officers to send his subordinates into their deaths.
..we must understand how hard it is to be the one to give the orders that will send your friends to their deaths, and how easy is the alternative of surrendering honorably and ending the horror. The essence of the military is that to be a good leader you must truly love (in a strangely detached fashion) your men, and then you must be willing to kill (or at least give the orders that will result in the deaths of) that which you love. The paradox of war is that those leaders who are most willing to endanger that which they love can be the ones who are most liable to win, and therefore most likely to protect their men.
In nearly all historical batlles prior to the age of Napoleon, the serf who looked down his spear or musket at the enemy saw another hapless serf very much like himself, and we can understand that he was not particularly inclined to kill his mirror image. And so it is that the great majority of close-combat killing in ancient history was not done by the mobs of serfs and peasants who formed the great mass of combatants. It was the elite, the nobility, who were the real killers in these battles, and they were enabled by, among other things, social distance.