Probably more war:
- Depending on the country who developed it, the risk of nuclear war could go up.
If I don't have to worry about nuclear retaliation, maybe I'm very confident in engaging in war. After all, my nukes will still work, and everyone else's won't.
- If the technology is shared equally to all countries at the same time, the risk of conventional war could go up.
Imagine the nuclear armed countries who are enemies of another nation with a bigger military. North Korea vs USA, Pakistan vs India. In these cases, nuclear weapons are a deterrence against the stronger opponent. Without this, the country with a stronger conventional force may be more likely to they think they'll win a war unscathed.
Sounds like the perfect reason to have different words. Who would want to type that out every time? I'm sure someone could spend several paragraphs describing the difference between fur and hair, or stucco vs plaster.
If you don't care about the difference between two words, then those words probably weren't invented for you. Someone else who works with that nuance on a daily basis probably really likes that they can sum things up briefly.