Administrators can do the following things that moderators cannot do:
1) Change group settings, eg turn group blog on or off, turn group forums on or off, change group status from public to private, etc
2) Post Annoucements
3) Change group avatar
4) Manage group members: ie kick/ban members, promote/demote members
5) Delete the group

Group moderators can do the following things that normal members cannot do:
1) Edit the Group Details, including the name of the group and group description
2) Edit, close, and delete forum topics/posts
3) Edit/delete group documents
4) Post Announcements