Occasionally, after applying an update (usually through Windows Update) the Start menuhas a small glyph beside the shutdown button, and a tooltip saying "shutdown and apply updates" Wouldn't a reboot accomplish the same thing --- is an full shutdown be the proper choice?
I've never used the "Shutdown and apply updates" option on a server. Installing the updates and restarting always seems to work.
I can't say I know too many people (if any) that ever use the "shutdown and install" option on a server. Everyone I know installs the updates either via WSUS or manually, then restart the server.
Yes for some reason that option presents itself rather then the more logical "reboot and apply updates". You can configure some of these options through Group Policy (don't force reboot while logged in, etc.) but I don't believe there is a option to show a reboot and apply option. This is a feature that started in XP and made more sense on the client computer, then made it's way to servers.
If server needs to reboot, you'll usually find a Windows Update icon in the systray (lower right) that presents a reboot and apply option.
Just to be clear, IF you've already installed updates, a standard reboot will still "apply" the updates.