Deleting a comment because it is insulting a person is moderation. Deleting a comment because you don't like it, it doesn't conform to your views or you find it outrageous, silly, inflammatory, false, fake is censorship.
Moderation is far more than that. Moderation depends on context - for example, deleting a comment like "$political-party is better than their opponents" from r/programming is "against freedom of speech", but is an example of good moderation, because political discourse is off topic on that forum.
Moderation is about setting the tone and scope of discussion. For many kinds of forums, this includes deleting comments that the moderators find outrageous, silly, inflammatory, and off-topic. Removing things that don't conform to their own views is however a faux pas, moderators are supposed to be neutral in the on-topic discussions, as their name suggests. False/fake are a more complex discussion, as there is no universal source of truth of course.
Now, for a completely open forum, such as Twitter or Facebook, moderation doesn't really make sense, since no discussion or tone is off-topic a priori (except of course for removing illegal speech).