According to the dictionary:
Contentment - a state of happiness and satisfaction
"Contentment, or the state of being content, is about peaceful satisfaction"
Happiness - feeling of showing pleasure
"Happiness is a sense of well-being, joy, or contentment. When people are successful, or safe, or lucky, they feel happiness."
"Happiness is self-contentedness. - Aristotle"
( more of my thoughts on this )