Broadly speaking in general terms, you can think of it as a question of authority and responsibility. Administrators have more authority than moderators. Both have duties they're responsible for, but their responsibilities differ in type and degree. It's like the difference between managers and those who work "under" them in terms of organizational heirarchy.

But the exact job descriptions might vary from organization to organization.

Well, some admins are also ZOS staff, Matt Firor is the President of ZOS while judging by his forum activity Adrikoth is an actual administrator on the forums.

The canned responses of the NameCapitolLetter users is annoying, but basic CS routine. You rarely get a non-canned response from someone who is just there to do a job.

I do not think you all are giving them credit where credit is due. A lower-level CS employee is not "just there to do a job," they are doing their job as permitted and required. They do not have the luxury of making or changing rules on the spot, but are responsible for carrying out the rules as laid out by others.

Are you all saying that you have never been in a lower-level position in a work environment, with managers and administrators over you, where you were required to follow the rules or else be reprimanded-- or worse-- for not following the rules?

In any case, this whole discussion really has nothing to do with ESO, and will probably be closed for being off-topic-- and rightly so.