After installing updates which require a reboot, the Windows 8 Power button shows "Update and Restart". What I really want is "Update and Shutdown". How can I get this option to appear? I didn't realize it even existed until I saw it on my system where only "Update and Shutdown" had been available. I gathered this happened because I did not install pending updates for a day or so. Shift/Ctrl/Alt clicking on the choices bring no new options.
There is a group policy which has been around since XP SP2 which will prevent this from showing up, but I have not found a way to force it to show whenever updates are pending. The thread No more update at shutdown? in Microsoft Community discusses this issue as well.
Digging further I found the registry key
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\WindowsUpdate\Auto Update\Power\OfferInstallAtShutdown-Final which looks related but could not find any documentation for it. It is set to 0x28 on my system. When I changed it to 0x01 it came back after reboot as 0x28. When I changed it to 0xff it stuck after reboot but neither option changed my Power button options.
Reading Minimizing restarts after automatic updating in Windows Update I see that Install at shutdown is a popular option. Is it not offered when the updates require more work after restarting?
This superuser thread is related: How can I install updates and shut down from the command line?
shutdown.exe /s /t 0 from the command line as suggested by @Vargas below installed the update and shut down as desired when Power>Shutdown did not. The real question remains which is how can this be done consistently through the GUI?