I think we can all agree that the reality that the term “genocide” is meant to represent — the systematic destruction of a race or ethnic group — is a horrible crime. Everyone is obviously against “genocide,” and that is precisely what makes it such a potent tool in legitimating war. Virtually any war could be presented as genocide, because the point of war is to use violence against an enemy group until they either submit or are destroyed.
Civilian deaths can’t serve as the criterion, because contemporary military techniques make civilian deaths inevitable. Even worse, it is difficult to distinguish between combatants and civilians outside the highly idealized context of two recognized nation-states facing off using only uniformed troops.
The difference, in both cases, is intention. They want to kill for the sheer sake of killing, while we do so with deep regret. They hope to kill the maximum number of civilians, while we regard it as tragically unavoidable “collateral damage.”
The parallels with the use of “terrorism” are striking. Again, we can surely all agree that the reality that the term “terrorism” is meant to represent — random violence for the purposes of terrorizing the population at large — is a horrible crime. But here again, it seems that war in general is terrorism by this definition. As is well known, in the ultimate “Just War” (World War II), the US purposely targetted civilians (including with nuclear weapons!), not for purely strategic reasons, but precisely to break the spirit of the population as a whole. How can we distinguish those campaigns, or subsequent ones like the carpet-bombing of Vietnam and Cambodia or “Shock and Awe,” from terrorism?
Again, the difference is intention. Terrorists kill out of motiveless malignancy, while we have a good reason. In other words, they’re evil, while we’re good — hence whatever they do is definitionally evil, and whatever we do is definitionally good.
For the purposes of political discussion, then, I propose that we redefine both terms. Genocide is a term for acts of violence by a state or state-like actor that is not allied with the West. Terrorism is a term for acts of violence by a non-state entity that is not allied with the West. In this respect, both belong to the legacy of Cold War political moralism — where “totalitarianism” designates political systems other than liberal democracy in countries not allied with the West, for instance, or “human rights violations” are, for all practical purposes, definitionally only committed by countries not allied with the West.
It’s like Schmitt says — a claim to transcend politics, as in the postwar attempt to translate politics and war into the sphere of morality, is one of the most aggressive possible political moves.
An und für sich 
Raphael Lemkin coined the term genocide in the 1940s because at that time there was no in international law for naming the government-sponsored killing of citizens based on their genos. In this sense, genocide is not an attack on another state. That is what war is. So, to me, the difference is clear.
The strict sense of the term and concept remain essential because without them even before the eyes of an international court genocide is legal. The paradigmatic case for Lemkin was not just the Holocaust but also the Armenian genocide. In both of those cases, as in most cases of genocide, the international community did not intervene until much too late. He hoped having a legal concept of genocide could change that.
For reference and for those unfamiliar with Schmitt’s argument:
“Nothing can escape this logical conclusion of the political. If pacifist hostility toward war were so strong as to drive pacifists into a war against nonpacifists, in a war against war, that would prove that pacifism truly possesses political energy because it is sufficiently strong to group men according to friend and enemy. If, in fact, the will to abolish war is so strong that it no longer shuns war, then it has become a political motive, i.e., it affirms, even if only as an extreme possibility, war and even the reason for war. Presently this appears to be a peculiar way of justifying wars. The war is then considered to constitute the absolute last war of humanity. Such a war is necessarily unusually intense and inhuman because, by transcending the limits of the political framework, it simultaneously degrades the enemy into moral and other categories and is forced to make of him a monster that must not only be defeated but also utterly destroyed. In other words, he is an enemy who no longer must be compelled to retreat into his borders only. The feasibility of such war is particularly illustrative of the fact that war as a real possibility is still present today, and this fact is crucial for the friend-and enemy antithesis and for the recognition of politics.” (The Concept of the Political, tr. George Schwab, University of Chicago Press, [1932]1996, pp. 36-37)
Dunno why we have to invoke a Nazi thinker like Schmitt here.
Because that’s where I first found the idea I reference in the relevant paragraph?
If I recall correctly, much of the International Relations writing on genocide (of the Samantha Power variety) focuses on the question of numbers (this is what Badiou was writing against, i think, in his Ethics book?) The problem, if I am remembering right, is that genocide seems to correspond with a “numerical grotesque”–6 million, paradigmatically–and thus a “count” should set the threshold of “genocide.” But that would have the effect of licensing the mass murder of so many thousands or millions below a given threshold. Thus, the adoption of Lemkin’s much more abstract and eclectic criteria, which have had the unfortunate effect of providing a pretext for more or less any act of Western aggression (while also opening up a crucial “negation of the negation” in cases that are clearly pre-“genocidal,” such as Gaza, and yet cannot be recognized as such in Western diplomatic discourse for complicated reasons). I’m not being very clear here, I worry: I suppose what I would want to add to the discussion is the question of “number” and “counting” vis-a-vis the question of genocide in the context of left metaphysics/political theology.
Long time lurker and fan here. Genocide can never be legal.
In international criminal law the term captures acts directed against “a national, ethnical, racial or religious group, as such”. All is in the “as such” so even wars against states can very well be genocidal if the requisite intention is made out. However you need a court with jurisdiction to make that declaration authoritatively and such a universal court does not yet exist.
Therefore the gap is not in the law but in the institutional architecture where some actors are powerful beyond the legal/illegal distinction. Indeed (Schmitt and Agamben are best at explaining this) their word has the force of law simultaneously with their force being beyond the law.