I've never fully understood, maybe somebody can explain, what's the difference between impact well sockets and typical sockets?

The forces that act on a socket vary between a regular socket wrench and an impact wrench. A socket wrench exerts a steady torque, while an impact wrench sends out enormous amounts of torque for a very short time, repeatedly. Thus, a socket designed for impact use would need both stronger materials (to prevent breaking) and ideally, a tighter fit (to avoid damaging the nut's corners).