Start-Stop vs HSD

"My car also turns itself off at a traffic light!"
This is a classic when someone is on the passenger seat, while driving.

Modern, non-hybrid cars have a start-stop system that shuts the engine down while standing still.

This is fundamentally different from an hybrid car:
A conventional car shuts the engine off after the car has stopped, and re-ignite it before moving again.
The HSD system works the opposite way: the engine shuts down before stopping and it starts again after the car is already moving.

Here is the detail of a stop at a traffic light.
Engine rpms in red; speed in blue.
The car comes to a full stop a 15:09:35 and starts again at 15:09:40:

The engine stops 30 seconds before the real stop, and starts again after the car is already in motion.