I understand how our moderators get elected, what they do, and so on. Beyond that, I know the moderator agreement, which basically clarifies the restrictions under which moderators operate, and that SE Inc. can terminate them at will, and that "of course" moderators have zero nada niente authority to "bind" SE Inc. in any matter.
Now: there can be two ways of defining a "community".
The first one is what "follows" from the things I listed above: there is a group of people that share a certain context. And that is it. There is no other "link" between all members of the community, and some moderator X could decide to never visit that private chat room (or even MSE), and only sync up with peer moderators for the place they are "working" on.
The second one is based on the idea that all (or at least a large majority) of the people sharing that same context go beyond and, and for example: actively organize themselves. As in: electing representatives that have the mandate (authority) to speak for the overall group. Or by establishing communication paths that ensure that all members of the overall group can be reached. In this setup, a moderator for community X always considers themselves also as a moderator of the overall Stack Exchange network.
I think: regarding the overall set of moderators on the Stack Exchange site, it seems to me that the first definition applies.
Question: is my understanding correct, or are things more complicated in reality?
And in case my first definition matches the current state: do you moderators think that should be changed? Or are you all happy about status quo?