I think this is more referring to the powers that are bestowed upon diamond moderators and trusted users.
There's little difference between the two roles except:
- Moderators act and behave in an official capacity on behalf of the community,
- Moderators' votes are binding - they take effect immediately,
- Moderators can view deleted content (such as comments), and have access to more information about a user
...but outside of that, that's about it. Also, those with a gold badge in a tag have a binding vote on duplicates, which make that power somewhat similar to a moderator's.
You can read a bit more about what diamond moderators' powers are and what their role is at this FAQ entry.