It's a wonderful question; by way of beginning, I looked up the etymologies in English, and "happy" comes from hap "chance, fortune," the same root which gives us haphazard, or happenstance. So in English also, happiness inherently connects to luck. A happy man was a lucky man, a fortunate one.
When, in disgrace with fortune and men's eyes,
I all alone beweep my outcast state,
And trouble deaf heaven with my bootless cries,
And look upon myself and curse my fate,
Wishing me like to one more rich in hope,
Featured like him, like him with friends possessed,
Desiring this man's art, and that man's scope,
With what I most enjoy contented least,
Yet in these thoughts myself almost despising,
Haply I think on thee, and then my state,
Like to the lark at break of day arising
From sullen earth, sings hymns at heaven's gate.
For thy sweet love remembered such wealth brings,
That then I scorn to change my state with kings.
Haply [happily], i.e. by chance he thinks of her, and the whole world changes. That's how to be happy.
Joy apparently comes from the Old French word for jewel, but is connected to something much more active: rejoice, enjoy, etc. Even from this one could paint a picture of happiness as occurring to us, whereas joy is something in which we are active, or at least something which we actively experience. I imagine joy in a deep sense is connected to creativity and to creation, though there's much to think about here.