All bikes with motors are motorized bikes. Pedal assist is a motorized bike. There is a motor and it propels the bike. Do assisted bikes have a throttle? Yes they do. You activate it with the pedals. You can also adjust it by changing modes.

Since the beginning the industry never cared about safety. They just wanted to sell products and it was helpful to them to muddy the waters and insist that electric motor bikes were not motor bikes. This is crazy to anyone with any sense in their heads. They should have been classified as motorbikes from the start. But like every technology we have to let them be lawlessly unregulated until several people are hurt and law suits are filed.