Censorship is merely the act of limiting access to information. It doesn't matter who is doing this. Yes, governments often do it, but so can private entities. An individual can even do it to himself, in the form of self-censorship.

Moderation is the application of censorship in order to modify a discussion. Once again, anyone could potentially do this, including governments. An individual can do this to himself, too, by selectively choosing which parts of a discussion to consume.

Hackernews is censored fairly strongly, and moderated "ok".