We honestly don't see much more than you all do. We have our Moderator's Forum which allows us to discuss actions that need to be taken when someone spams us, or new people sign up and have a vulgar screen name...etc.
A lot of the times if I'm away at school and miss a thread before it's deleted I never DO know exactly what was in it...because if it's deleted it's essentially GONE. That happens in my forum a lot because we have four moderators. So if one of us deletes something we try to keep the others informed.
As far as what the site looks like...its the same format for us as it is for you. Anyone can go in invisible mode...but it doesn't make anything appear differently. I'm not sure if that's what you're referring to or not. Hope it helps!
I think that the only difference is that at the bottom of the thread we see administrative options and we can delete, move and split threads. Otherwise the site looks exactly the same with the addition of the Moderator's Forum that we can access.