I think that's in the legal context: the US government is bound to the 1st Amendment, which has usually been interpreted broadly to apply to (almost) everything the government does. So when the US government does the censoring, it's often questionably legal. However, private organizations aren't usually bound by the same rules, so there's no law against a private organization doing the same thing.

I suppose we can call it "censoring" in both cases, but usually only one of the cases is an actual violation of the law.