Short answer: Hang is the name of the original instrument by one Swiss workshop, handpan is the name for the whole family. What people buy today is a handpan.
The Hang was created by PANArt in Bern and presented in 2000. The name belongs to them, and PANArt stopped making the Hang in 2013.
Makers around the world build instruments on the same idea: a ding in the centre, tone fields around it, one scale. All of them are handpans, and in everyday Russian many people still call them "ханг".
The scale, how clean and stable the notes are, the sustain and the steel. Listen to a recording of the exact instrument, not a demo of the model.