Hi @razhael, this is a great question, with a frustratingly circular answer, I'm afraid.
The use and overuse of "cyberattack" and "cyberwar" largely came from government and policy making circles. These terms were and are convenient metaphors for military and policy/international relations people, because they fit the intellectual paradigms that already exist in those circles. This is extremely useful for military and policy people, since it allows them to sound authoritative on topics about which they know little* (we need to preserve cyberdeterrance) and since such terms make pushing for bigger budgets for their work easier (we have a cyber gap!).
Unfortunately, the "cyber" armed conflict metaphor and the scare tactics that go with it are part and parcel of the term, since it was largely popularized by people in government who wanted to increase their own influence by pushing the idea of "cyber" as a "fifth domain" of conflict (alongside air, sea, land, and space). Since ignorance is widespread, the first group who could convincingly articulate a policy paradigm for nation state competition and conflict on the internet was going to do well for themselves.
So, the situation where a policy maker has to be talked down from advocating physical retaliation for a hack is sadly ironic, since the whole purpose of "cyber" and it's over-use was to stoke fear and raise the profile of "cyber" as a paradigm of conflict, alongside traditional, "kinetic" forms of conflict, without actually having to develop any new theories of conflict (Jomini and Clausewitz in space! Jomini and Clausewitz in cyber! I am a military policy intellectual!).
The cyberreality is that 99% of cyber is espionage, and the other 1% is sabotage (think Stuxnet, or Flame). The word "cyber" is really just a product of a budget fight between intelligence community and the armed forces. Re-framing "cyber" as a conflict issue, rather than an intelligence issue, became increasingly vital for the military bureaucracies as the internet became more central to, well, pretty much everything that humans do.
All of these terms have their own social lineages, however. Terms like "breach" or "compromise" tend to be used in the private sector, because information security people in the private sector are strictly defensive and care exclusively about protecting their own networks and users. The term "hack" came out of the model train club at MIT, and generally refers to getting a system to perform an action that was not intended by the system's author(s). So, hack is a practitioner's term, since unlike "cyber" (which refers to where the action is happening) or "breach" (which refers to what just happened to you), "hack" actually says something about how one goes about compromising systems. Hackers misuse rules (usually software) that were written by others, in order to subvert the intent of these rules, while technically complying with them. This is the essence of hacking.
*Note: There are obviously some very knowledgeable and talented software engineers and hackers in government, but these are typically not the same people who are running around talking about "cyber" with metaphors they lazily borrowed from IR policy.