alt Hacker NewsE-Bikes are sold & regulated in "classes" (at least where I live in the US).
A class 1 e-bike is pedal-assist and stops assisting beyond 20mph (mine, for instance, tapers off starting probably around 15 mph).
A class 2 is the above, plus a throttle.
A class 3 is anything that assists over 20mph. The "basically motorcycle" set exists here.
Your class 3 definition is inaccurate. Class 3 is limited to 28mph and cannot have a throttle, only pedal assist.
Anything that doesn't fall in one of those classes is a motorcycle that is not street legal and can only be rudden of private property (unless you can convince your DMV to give you registration as a motor vehicle.)
This can vary somewhat from state to state, but most states have adopted or are moving to adopt these classes.