HN is a private organization and has every right to do anything they want with the content.
My only request was for feedback.
Bit of a side issue, but that's an interesting statement, I've never heard that before. A quick google doesn't seem to back that up, so I wonder what I'm missing, or why you said that?
I suppose we can call it "censoring" in both cases, but usually only one of the cases is an actual violation of the law.
I'm not American. It's just the best explanation I can come up with why this view is so common.
On a forum like HN freedom of speech does not apply, because you don't have a right to post here. The first amendment only applies to the government, as it relates to your property, public property, or other private property that you've been granted the right to express through (eg the NY Times).
You don't have a right, for example, to walk into your neighbor's house and exclaim your position on communism.
For another private party to stop you from exercising your freedom of speech, eg in your yard / on your property, they'd have to initiate violence, and properly that is already illegal. It's the government's job to protect you from that force, and by doing so would be upholding your right to free speech (if they fail to do so, they're not protecting your rights, and that can be government censorship by proxy).
And in regards to private context, it also is dependent on what you've agreed to, such as in signing a contract. If you join a community, whether Hacker News or a housing development, and have agreed that you may not fly a flag in your front yard or use verbal abuse (on a forum), then that's a choice you've voluntarily signed on to.
But you may not be able to avoid it. If a forum is the popular forum, you either post, or never be heard. You have to post there to get heard. So the "private company" can choose what is heard or not. That is censorship. Not illegal, as many said, but censorship. With all the bad results.
HN censors people every day, as is their right. My account right now is under the influence of a slowbanning for what reason I have no idea.