I've been thinking lately that what distinguishes "War" from "war" is the alignment between the targets of violence and the objects of the conflict. In conventional wars violence is directed at the warmaking capacity of the enemy regardless of the overall object of the war itself, partly in an effort to insulate civil society from the destructiveness of violence. In less conventional wars, violence is applied directly to the object, and warmaking capacity is often only targeted indirectly.

Examples from opposite ends of the spectrum: The cabinet wars of the eighteenth century, where being placed at a military disadvantage through the loss of a fortress or a battle was often enough reason for one side to give way and settle whatever political, dynastic, or economic dispute led to the military contest; Vietnam, where political opponents of the communists and their supporting populations were targeted directly.

Obviously, because we are speaking of a spectrum here, the examples bleed into each other, and you can always find an exception, but this idea of using violence to directly gain your objectives (rather than indirectly when two militaries clash) seems to me to be a useful analytical tool.