Yeah it varies entirely by state, the last time I checked in North Carolina there’s a legal definition for “moped” which has a maximum speed fo 30mph, an engine of no more than 50ccs displacement, no external shifter controls, etc. And these are legal for road use without registration or a motorcycle license. I don’t know how or if they’ve adopted laws about electric assist bicycles, but I imagine if it can go more than 30mph under its own power it would require a license plate and a motorcycle endorsement to operate.