Spoonfeed me what exactly "On Hit" means. What's the difference between "I On Hit" and "II On Hit"?

If I that means what I think it is, does that mean that I can't proc "II On Hit" if I hit an enemy with only one coin?
What if I clash with an enemy that has more than one coin - if I lose, I'm left with only one coin, can I still proc "II On Hit"? What about "II Heads Hit" in that scenario?