A censor was a government employed entity where you had to present your text BEFORE you could publish it. Book, newspaper articles, things like. It was in heavy use in the European kingdoms and republics (e.g. during Napoleons reign).
You had no choice there: would you not censor and publish, then hefty fines would be one you. Sometimes even leading to death, e.g. look up "Der Hessische Landbote" from Georg Büchner, a tract against monarchy and feudalism.
So censorship has two keys: mandatory prior check, fines if you publish a text without that.
Moderation however is to keep your channel in a sane tone. It is something you do out of your own will, e.g. to cut down on flaming. And there is no government entity involved that checks the text in question. It is, after all, not identical to censorship.
My guess is that anarchist minded people, that (wrongly) believe that human groups develop organically in a nice way, have a problem with moderation. And then they seek some word with an extremely bad connotation and just use that instead. Just like some politicians use these days "terrorist" in plethora, even when "murder" would describe it better.
IMHO users of "censorship" term often want to manipulate us.