Most e-bikes come in the form of a Pedelec or pedal-assist, which monitors the input of a rider and assists as much as possible up to the region-specific top speed.
Less common are Twist-n-Go models, which allow riders to operate the input of the motor from a switch (or even a throttle). Most places classify these as a moped and you may need a licence, insurance, and a full helmet to ride them.