Alternatively, you can get a convenient list of commands coupled with quick descriptions (as long as the command has a man page, which most do):
apropos -s 1 ''
-s 1 returns only "section 1" manpages which are entries for executable programs.
'' is a search for anything. (If you use an asterisk, on my system, bash throws in a search for all the files and folders in your current working directory.)
Then you just grep it like you want.
apropos -s 1 '' | grep xdg
yields:
xdg-desktop-icon (1) - command line tool for (un)installing icons to the desktop
xdg-desktop-menu (1) - command line tool for (un)installing desktop menu items
xdg-email (1) - command line tool for sending mail using the user's preferred e-mail composer
xdg-icon-resource (1) - command line tool for (un)installing icon resources
xdg-mime (1) - command line tool for querying information about file type handling and adding descriptions for new file types
xdg-open (1) - opens a file or URL in the user's preferred application
xdg-screensaver (1) - command line tool for controlling the screensaver
xdg-settings (1) - get various settings from the desktop environment
xdg-user-dir (1) - Find an XDG user dir
xdg-user-dirs-update (1) - Update XDG user dir configuration
The results don't appear to be sorted, so if you're looking for a long list, you can throw a | sort | into the middle, and then pipe that to a pager like less/more/most. ala:
apropos -s 1 '' | sort | grep zip | less
Which returns a sorted list of all commands that have "zip" in their name or their short description, and pumps that the "less" pager. (You could also replace "less" with $PAGER and use the default pager.)