Out of curiosity, I'm just asking if a moderator is global or site-based. In other words, will a moderator only moderate a specific site or moderate all SE sites? And is there any privileges for moderators (e.g. Gain lots of reputation instantly)?
Diamond mods are elected or appointed on one site. They got the diamond only on this site.
Those who have diamonds on all the sites are community managers, developers, or other SE employees (some of employees have the diamond only on this site - MSE, and some are not given diamonds at all).
As for getting reputation, there is no difference between mods and usual users. But mods have all the possible privileges regardless of their rep.