The short answer is yes, e-bikes work through pedal assistance; there is no throttle (unless you're in the US where this can feature on some models). The e-bike will deliver power proportional to how much you are putting in yourself.
However this is only up to a point. In the UK, e-bikes are limited to providing pedal assistance up to 25 kph (15.5 mph); above that speed you will be propelling the e-bike under your own steam.
In the US, it's a bit more complicated, as the laws vary from state to state. The Bicycle Product Suppliers Association has sought to clear up the murky legislation with a three-class system — each limited to 750-watt motors.
Class 1: the motor is strictly pedal assist and is limited to 20mph
Class 2: can provide assistance whether or not the rider is pedalling, and is limited to 20mph
Class 3: the motor provides pedal assist, is limited to 28mph, and must be equipped with a speedometer.
Our friends over at People for Bikes have complied a complete guide that breaks down the rules state by state.
Read more: Electric bikes and UK law: what you need to know