Hi ... happiness is the state of being happy...while joy means great happiness and pleasure. Reference: Longman Dictionary of Contemporary English

Happiness is an emotional state of well being characterized by positive intense joy. Joy is just an emotion of happiness. So, Happiness is an state while joy is just to be happy. Like, you can say anybody joy with love but not happiness. Happiness can be classified as verb or gerund while joy is a noun or more specifically concrete noun.