"Well-being" versus "happiness"

Well-being represents how well someone is faring as a person. This could be with regards to someone's health, mental health, or the environment in which a person (usually a child) lives in. It doesn't necessarily imply that such a person would be happy, simply that they live in a state that's "in their best interests."

Happiness on the contrary is that fleeting thing which people always desire but may or may not always be in their best well-being. I hope that answers your question.

Well-being is the state of being comfortable, healthy, or happy.
You can speak of well-being for an happy person, but a happy person can also not be healthy.

I would summarize it succinctly as:

• 'Well-being' is a state of body.
• 'Happiness' is a state of mind.