Joy and happiness are two words that mean the same thing. The only difference is that there might be a slight difference in their connotation. One difference between the two words is the amount of usage in regular conversations. Joy is not used as often as happiness.
The word happy is used far more than pleasure and therefore, so is satisfaction. Joy probably means a little bit better feeling of emotion than happiness, mainly because happiness is used so often. Over time, the word joy has happened to include a stronger meaning because happiness is so overused. Since joy is not used, it is saved for the times when there are extraordinary occasions of this feeling like when someone gets married or has their children.