That's why the distinction made by the dictionary definition AFAIK is not made by form, but by actor. Censorship is done by a public authority, moderation is done by a private entity.
I've said elsewhere that Twitter might be public infrastructure. The distinction is still clear though.
(Me personally, I think it should not be allowed for individuals to own the wealth of small nations, much less command it. But that's a different topic)
Well, I didn't say 'government censorship', and I think it's redundant. Which might be just me, but you can Google "difference moderation censorship" and see that this is a generally accepted view.