The moderator usergroup is to attribute the user group permissions that you have set. You may choose to create another user group for junior moderators with a lighter setting and a senior moderator usergroup with more liberal settings.
The moderator attribution is a different animal, which gives a per user permission and functionality.
Then there is the administrator attribution, which you can use to give admincp access to your moderators and give them specific thigns to manage. Like moderating new users, bans, view spammer logs & statistics, etc. Even though the administrator attribute provides essential functionality for moderators it should only be given to people you really trust. Because a lot of other permissions are lumped in there which can be destructive to your site and can potentially be used to take over your site.