Althought the Pi can be shutdown, like any other computer. In my experience, the only way to restart it while off and connected to power is disconnect and reconnect power.
Many people, don't believe the Pi can be shutdown, but that just is not true. From terminal or SSH remotely
will shutdown the Pi, or from the GUI you'll have the option of Logoff, Reboot, Shutdown, etc., but there is no WOL support. If you want to shut it down and remotely start it you'll need something else that can remotely cut/provide power like a smart plug wifi outlet. Once the Pi is off, if you turn the smart plug off and back on, the Pi will start up.
If you just want to restart the Pi
works without issue with no need to disconnect power at all.