It's a nice distinction. I wonder whether we can go further though, and not even need that distinction. Here's my take on it.

Any human endeavour is worth its salt if it succeeds at discovering and expressing beauty. It can be a mathematical proof, a theory in physics, an elegant algorithm, a painting, a dance, a novel, a relationship - the list is as endless as the number of ways humans can come up with, and can be as deep and complex and subtle as they wish to make it, but it always comes back to finding and expressing beauty.