We had a class called Arts and Crafts in elementary school, and nobody, neither the teachers nor the students, could explain the distinction. I grew up assuming art was painting and craft was sculpting. Or perhaps art was making things and craft was washing our hands afterward. These days, I understand the difference this way:
Craft is everything on the canvas, and art is everything outside the frame.
Every brushstroke of the Mona Lisa is craft. Its color palette is craft. Is portrait composition is craft. The expression on her face: alas, it is craft. The art lives in every secret teased by her inscrutable glance. The art lives in our obsession with her hands, her smile, her personal life. Her mystery, her history, her conspiracy.
As it goes in oil, so it goes in ink and strings and code. So it goes in our relationships, too.
Art requires something left unsaid. Everything else is craft.
Most classes teach craft.