shut down, shutdown

Two words as a verb, one word as a noun.

Use shut down to describe exiting the operating system and turning off the device in a single action.

Don't use shut down to describe turning off a device or as a synonym for close.

Examples
To turn off your computer, select Settings, and then select Shut down.
Use the Shut down command to safely close open apps, shut down Windows, and turn off the device.
Many computers turn the power off automatically.
The accidental shutdown might have damaged some files.

See also
Describing interactions with UI
turn on, turn off
sleep