I have 500+ reputations on Stack Overflow which gives me the privilege to review some posts on SO.
So, can I consider myself a moderator of Stack Overflow?
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In addition to "moderator" almost always referring to diamond moderators (usually the elected community moderators, though the same privileges are held by many Stack Exchange staff), the review queues that one has access to at 500 reputation on sites like Stack Overflow are mostly advisory: they flag issues for the attention of higher-reputation users, such as those with the close-vote privilege, and diamond moderators.
As such, these queues assist (quite a bit) with moderation, but do not really perform it directly.
People who are not diamond moderators, but do things to help moderate and curate the site (including flagging, upvoting, downvoting, and voting to close) are often informally referred to as "curators." If you're doing that, you could accurately describe yourself in that way.
"Moderators" almost always refers to diamond mods. The confusion with referring to non-diamonds as moderators arises mostly from the "access moderator tools" privilege at 10k, which dates back to when those users could see flags. Since they can no longer see flags, and it's confusing, we should probably just abandon the moderator wording there and reserve the term for diamonds.
So while it would technically be grammatically correct to call yourself a moderator since you assist in moderating the site, it's incorrect in the context of the site and the roles of people involved.