There is a layer called [ACPI](https://en.wikipedia.org/wiki/Advanced_Configuration_and_Power_Interface#Power_states) which is how the software running on the computer talks to the hardware about many things including power states. So using that, the Operating system tells the motherboard that it wants it to do a restart in much the same way it tells it to do the shutdown. Also in a restart while most everything is reset as if it was switched off and on again, power isn’t just cut off (at least not to the bit of hardware that is responsible for power management)
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