A member of our Sangha asked a question which inspired me for this post. "Do you think there is a difference between inner-peace and happiness?"
I believe there is a difference but they are definitely interconnected. To me, happiness is an emotional response to conditions and events. Inner-peace is a mindset (for lack of a better term) which allows us to accept conditions, whatever they may be, and can be the root for happiness. The Buddha himself valued inner-peace above happiness.
With a clear mind and inner-peace we can accept suffering with less stress and figure out the root cause of it. That lessening of stress inevitably leads to happiness. Of course, we as humans aren't always happy. We always have a desire for what "is best in our view." Though through inner-peace, we can realize that we are able disregard what "is best in our view" by extinction of ego and desire. Therefore, happiness ensues.