One of Timothy L. Thomas's terms is "long-range electronic reconnaissance" which is a better description of most cyber activities than war. When China accesses our systems, it is gain intelligence, industrial secrets, or just tests our electronic defenses. Cyber war would consist of military operations with the goal of disabling, controlling, or destroying systems to aid an overall military effort or accomplish a standalone mission to inflict violence for political effect (the equivalent of firing off a few cruise missiles during the 1990s).
Most of what we have seen, with very few exceptions, has been cyber-reconaissance or just plain espionage. Cyber war, on the other hand, is a different matter. H. Lucien Gauthier III describes a bit of the theoretical challenges:
In cyber-warfare we are growing our capacity to both wage and defend against this type of warfare. But, we have not even started to get close to being able to define where it is that a kinetic, or real world, response is warranted. If a Nation-state purposefully destroyed the Hoover Dam, it would be unequivocal that we would have to respond in kind. However, in a cyber-attack, if the NYSE was taken offline we would 1) struggle to say who was guilty of the attack and 2) struggle to prove the efficacy of a kinetic/real world response to the attack—does utter economic devastation demand a nuclear response? Is a way of life shattered the same no matter if the cause is nuclear or electronic? We have this ‘gray area’ in our use of force continuum because of the novelty of ‘warfare’ in a completely synthetic domain (online). We do not have thousands of years of experience to fall back on, or to show a precedence to warrant our course of action, or to make the decisions readily understood by the guy on the street. However, to both effectively protect our infrastructure and project force in this domain we have to have a clear ethical and philosophical foundation from which to act.
While there are historical parallels (such as the use of strategic bombing, sea power, or limited uses of force), there are specific technical aspects of the usage of cyber tools for force that are specific to the domain that makes it difficult to transplant operational understandings valid to one domain to the other. A good deal of contemporary research and writing on cyber warfare deals with these unique issues. But the foundational frameworks of integrating it into our dominant understanding of warfare are more common in other non cyber-specific studies like David Lonsdale's 2004 work.