Got it fixed- Permissions on Moderator turned off.
It is strange that moderator permissions also affect the admins permissions. Not real logical--they should be separate permissions--don't you think?
Moderators and administrators are different roles but it is possible to be both, and that's how the default administrator account is set up. They are a moderator and receive the default permissions for a moderator, they are also an admin and receive the default permissions for an admin.
Generally the permissions are cumulative. This guide explains how they work in more detail: