Start/Stop – Behavior

Hello, a question that came to my mind only after my test drive yesterday : I noticed that the start/stop automatic starts the switched off engine only when the foot presses down the accelerator pedal. Is that always so or is there a connection to the autohold function of the parking brake? For explanation: with my current vehicle with mechanical parking brake, the start stop automatic is controlled via the brake pedal. So when I leave the brake also the engine starts again. I like the brake pedal variant actually better, because it is a little faster. However, you have to leave the foot on the brake, what with the variant with the control by the gas pedal does not apply. But this actually only makes sense with Autohold. Therefore the question. can someone help me further? Many greetings Quwe