The distinction you are trying to make is impossible to make in practice.
I don't want to see holocaust denial bullshit. Others might not have a problem with seeing it. Every sufficiently large space will contain at least one person who wants to post it and is therefore OK with seeing it. Is it moderation or censorship when a space I share with those people decides not to carry such content? The mods may not want to see it, and as it happens I don't want to either, but I've not actually /told/ them I don't want to. They've simply assumed on my behalf.
The same applies to any subject you might pick, no matter how controversial.
There's no per-person per-subject way to opt-in or opt-out that can possibly scale. I don't want to have to supply every online space with an exhaustive list of horrible things I don't want to see; and flagging after the fact doesn't solve this either since I also don't want to see those things even once before I get a chance to express my desire to not see them. Those cookie opt-out boxes with giant lists of vendors that everyone loves to hate? Imagine that but everywhere and for every subject. That's what exhaustively expressing my preferences would look like.
One approach that does scale is to allow the owner of a space to make filtering decisions on my behalf, and if my preferences don't match theirs in a way that is important to me, well, I can go elsewhere or make my own space. This is what we have now. But it's still someone deciding for me what they do not want me to see; they may or may not have my best interests in mind, but in your proposed classification, this is censorship.
Worse, though, some people /really/ want to parade stuff I don't want to see in front of my eyeballs - they believe the problem is that they are simply not shouting loudly, frequently enough, and if they were just allowed to preach to me one more time, I would convert. Compare the person elsewhere in this comments thread arguing for their right do "do business" everywhere currently moderated. Those folk are strongly motivated to make arguments containing combinations of words that will result in their bullshit being paraded in front of my eyeballs yet again. They will try feeding different combinations of syllables to the owner, the moderation team and/or anyone who might exert pressure on them, in the hope of rules being relaxed. One such possible combination of syllables is "This is censorship! I am being censored!" It may even be true, for whatever definition you prefer! Regardless, it will be attempted. For some, it's their hobby and/or job. They devote all available time to doing this. Slow drips of water, given sufficient time, wear down stone. If I don't push back even a little, all spaces I frequent will become filled with content I do not want to see. Is this censorship? Am I a censor?
Personally I see the moderation/censorship divide as one of those irregular verbs English is so full of, conjugated approximately like so: I am making my preferences known; you are moderating; he/she/it is a censor. The "our glorious homeland / their barbarous wastes" image frequently seen on social media is another good analogy for what frequently happens.
At the end of the day, though, call the practice what you will, but despite our best wishes, entirely uncensored spaces do not look like a university agora filled with enlightened folk freely exchanging valuable ideas for the benefit of mankind. They look like 4chan's /b/. I am glad such spaces exist, but I would be very sad indeed if every place on the internet was like that.