The question of existential risk is intentionally formulated as a very large conception that is concerned with risks to humanity on the largest scale — the possible extinction, stagnation, flawed realization, or ruination of Earth-originating intelligence. An existential threat (as the term is commonly employed, and in contradistinction to an existential risk) may be considered a relative existential risk, that is to say, an existential threat that constitutes a risk to concerns less comprehensive that the whole of humanity and humanity’s future. Individual human beings face existential threats, as do particular business enterprises, cities, nation-states, and social movements, inter alia. In short, any existing object that faces a threat to is continued existence may be said to face an existential threat.
When nation-states (or, before the advent of nation-states, their predecessor political institutions) that view each other as existential threats become engaged in a war, these wars typically escalate to become wars of extermination. A war of extermination is a particular species of the genus of warfare, uniquely characterized by systematic effort to not merely defeat the enemy, but to annihilate the enemy. Thus wars of extermination are also called wars of annihilation.
Another way to formulate the idea of a war of extermination is to think of it as a genocidal war. Genocides can be carried out in the context of war or in isolation (presumably, in the context of “peace,” but any peace that provides the context for genocide is not a peace worthy of the name). In sense, then, the ideas of war and of genocide can be understood in isolation from each other — war without genocide, and genocide without war — though there is another sense in which genocide is a war against a particular people, i.e., a war of extermination.
It is worthwhile, I think, to distinguish between the Clausewitzean conception of absolute war or the more recent conception of total war and wars of extermination, although this distinction is not always made. Absolute or total wars refer to means, whereas war of extermination refers to ends. Means and ends cannot be cleanly separated in the unkempt reality of the world, and the means of total war is one way to bring about the aim of a war of extermination, but a war of extermination can also be pursued by less than total means.