I agree that it's an important point that the punishment doesn't actually have to ever happen in order for the deterrent to work. Agree 100% on that. Nor do I think that I'm really saying that there isn't a distinction - what I'm arguing is that the distinction is which side of the coin you're looking at.

However, to split another hair, the WW2 example that you mention (I didn't see the original mention so I may be wrong about this) depends strongly for its deterrent effect on the fact that the US actually did drop atomic bombs on Japan, which created an example for the world to look at and learn from. I don't doubt that there would be a deterrent effect merely by demonstrating the bomb on fake houses and people, but actually dropping the bomb on populated areas probably greatly increased the seriousness with which everyone takes the atom bomb.