E-bike is a whole category, from bikes that offer pedal assist only and don't see speeds that are really higher than normal bikes, just offering higher speed for lower human effort all the way up to e-bikes that are like you said just light motorcycle.

But regulation and safety needs vary widely depending on category.

This is an e-bike: https://ride1up.com/product/roadster-v2/

So is this: https://www.eskuta.com/products/sx-250-series-iii-eapc-elect... (at least it's being marketed as one).

Really, we just need more terms. But it'd be nice if we could keep the label e-bike for the...bikes. Not the light motos.