To me hand winding is not having the wire machine guided, so either you move the wire by hand or the bobbin.
I also think if you have a programable winder, and set it to imitate winding my hand, it's probably the same thing. I think it's fair for a boutique winder using such a machine to call them "hand wound".
Not hand wound would be a fully automated winder... load the bobbin and press start.
It's like "hand knitted" sweaters. They don't have a person sitting there with knitting needles, they are operating a knitting machine, which is sort of like a loom. It's a machine, but the person is moving the carriage by hand.