I agree with the poster that there is no such toast as "На здоровье". Why are НА ЗДОРОВЬЕ and ЗА ЗДОРОВЬЕ so misused, and what is actually the difference between these two prepositional phrases?
On the one hand, you say За здоровье! if you want to propose a toast in Russian. It means "To your health!"
Here are a few more examples of the toasts:
За встречу! = To our meeting!
За успех! = To success!
За новую работу! = To the new job!
On the other hand, you say "На здоровье!" when you offer food to your guests, for example, Кушайте на здоровье! (Eat for your health).
Also, when someone thanks you for food, you can say "На здоровье!" instead of "Пожалуйста".
- На здоровье!
(Thank you. You're welcome.)
This is all very simple if you know the difference, right?