It's a question of what is meant by the term censorship. In the strictest sense, moderation and censorship are very often the same thing. If for instance, I post something terrible in a comment on here, and the administration of HN deletes that comment, then that's censorship.
However, when most people talk about censorship they're using it not in the strict sense, but rather as a shorthand for someone violating their first amendment right. In this case this is really only a crime when it's a government entity doing it, although people don't typically differentiate between the government and any large organization, which technically are legally allowed to censor you on their platform or property.
There's a larger discussion that needs to happen with regards to censorship. There are two extremes at play here, on the one hand there's the absolute freedom stance of literally nothing censored (only example I can think of for this is maybe the dark web, but really everyone censors if only a little), even shouting fire in a crowded theater or posting child pornography. On the other extreme is the absolute censorship of someplace like China, where only permitted thoughts and expressions can be posted. The US and most of the rest of the world tends to fall somewhere in the middle.
The big struggle right now is that everyone has recognized that there's clearly some kind of problem. We're seeing unprecedented levels of misinformation, and a frankly weaponization of social media both for profit, and for international politics. I don't know that anyone has a good solution for how to address that problem, but the pendulum seems to be swinging towards a more censorship focused response.