The two are not totally interchangeable, although both are nice things to say to people.
To wish someone good health literally means that. You are hoping that they remain safe and healthy in the future. You might drink to someone's health as well. This is when you toast them usually with alcohol. It would be quite common at birthdays, for example.
But to wish someone well is usually when they are starting out at something new. If your friend is moving to a new job, you'd wish him well. If a couple has just gotten married and are starting a life together, you'd wish them well. It basically means "I hope this thing you are about to begin is successful in the future."
Hope that's useful!