Peace is a condition of nonresistance to external circumstances. A condition of not desiring anything you don’t already have. Peace is the mental state of no suffering as taught by the Buddha and Jesus.
Happiness is genetic and consequently not subject to changing external conditions. It results from a genetic reward for performing altruistic acts, such as a good deed or love of neighbor, as taught by Jesus.
Well-being has to do with pleasures derived from external circumstances. While this state is commonly taught by popular psychology it is subject to ever changing external circumstances. Consequently well-being is always conditional and its emotional rewards are of low quality compared to genetic happiness.
The proof of these states can easily be verified by you.