What is the difference between Approve or Approve for Optional Install In WSUS
According to New in Windows Server Update Services 3.0, Microsoft extended the API to allow for 'creating approvals for “optional installation”'
These API extensions for "advanced options" aren't exposed through the GUI so that is why you only see this optional option through PowerShell:
"New APIs have been created for use by advanced management tools (such as System Center Essentials). These features are not exposed in the WSUS administration console."
These optional installations differ from regular approvals in that you don't install them via Windows Update, but instead through Add or Remove Programs. I think from Add or Remove Programs you then click "Install a program from the network" but I have not done this personally.
The approve option in the GUI is the same as the regular approve option through PowerShell.