What is the difference between the default groups on Mac OS X?
Regular OS X users are put into the staff group.
Admin users are put in the staff and admin groups. The admin group can do some things that other users cannot do. e.g. Write to the /Applications folder. If you want to put an OS X user into the admin group you should do this by designating him as an admin via System Preferences->Users & Groups.
root is the only member of the wheel group, and should remain the only member. If you have to do something that requires wheel, you should use the command sudo.