"To God a heart of flame,
to others a heart of love,
to myself a heart of steel."
Happiness is temporal and can be taken away because it is dependent on happenings (why else is it called happiness?). When good things happen, you experience happiness, but the moment the circumstances change, that happiness disappears.
Joy, on the other hand, comes from the inside and can't be taken away as long as you hold on tight to it. It does not rely on the external circumstances and it doesn't matter who you are, where you are, or what has happened to you. No matter how bad a plight you find yourself in, you can still have joy.
The joy of the Lord is my strength