As I think about this, weapons and tactics only define ways of fighting, not types of warfare.

Whether one is fist fighting, knife fighting, gun fighting or nuke fighting; the weapon only describes how one is fighting, not what type (genus and species) of war one is waging.

For me, I like to use "populace-based conflicts" and "state-based conflicts" as the two broad "genus" of conflict. The first is either "intra" to some state or occurs where there is not state structure at all. I do not believe that Clausewitz applies very well to such conflicts and many of our frustrations with this family of conflicts is due to our desire to force them to fit within a Clausewitzian framework.

State-based conflicts are "extra" or between two or more systems of governance (and the Social Trinity - rather than his "remarkable trinity" - of Clausewitz of "Government-Army-People" works fairly well to describe in simple terms such a system), seek to violently exert their will on one another. Apply Clausewitz vigorously.

Typically we end up dealing with blended conflicts of state and populace-based; or that begin as one and morph to another. It remains the supreme task to know what kind of war one is in - and when it is not war at all.