A pyrrhic victory and a loss are colloquially synonyms.

If America had launched nukes during the cold war, the USSR would retaliate. Maybe via submarine-launched ICBM, maybe using a dead man's switch; methodology is irrelevant, because the question is this: If both countries end up radioactive desert, which country would be declared the winner? Or is it possible for neither country to be the definitive winner of a war?

Right - the US didn't just win. They've achieved victory at least 20 times so far!