What you're talking about is clearly censorship and not moderation by the OP's definition - "blocking speech that both sides want to hear".

Your link is actually great for his point: people in power (OnlyFans and Meta) blocked something that both sides (their competitors, and their competitors' users) wanted to hear - otherwise they wouldn't have needed to block it. (For the sake of argument, I'm assuming that the lawsuit's claims are true - I have no idea if they are but it's not pertinent to this point.)

OK - it is not a sharp distinction - but can't we work with shades of gray? It becomes a no true Scotsman otherwise.

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.

In this day and age when not only companies, but individuals command the wealth of small nations, is that truly a clear distinction?

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)

So...don't allow individual to command the wealth of small nations and all these problems go away.

Wait, really? Then why do we say 'government censorship' ... that would be redundant.

I don't think that definition works.

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.