The Shutdown command does a controlled shutdown of the device's Tomato firmware (Linux OS). After shutdown, the Tomato router/device will power off. You must power cycle the router to power it back on.
NOTE: Since Release 2020.8, clicking Shutdown will prompt a second popup to confirm the selection. This was introduced to create a visual differentiation from the reboot function, as the two links sit next to each other. The wrong button could potentially be clicked by mistake.