I want to know whether the same set of moderators on a main site are the moderators of its meta, or do separate sets of moderators exist for each of the site and the meta.
If the latter is the case,
- Can a person be the moderator of both sites?
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Moderators (elected or pro tem) on a main site also moderators on its meta site.
So there are not two groups of moderators in that sense. The meta sites are however also patrolled by employees, for example for the reported bugs and feature requests and the occasionally spun out of control policy discussions. When they are at it they might moderate as well.
The only difference maybe is this site, Meta Stack Exchange. That has no main site to start with and it's moderators are only employees from the company Stack Overflow (formerly known as Stack Exchange).