Censorship is the removal or blocking of speech, moderation is a broader term that can include practices like flagging content without removing or hiding it completely.
The state actor distinction in the US is only important when deciding if a party is bound by the First Amendment. My speech is protected from government censorship, not from censorship by a private company.
[1] https://publicknowledge.org/content-moderation-is-not-synony...
I guess ironically some of the people trying to equate the two are doing so to suppress discussion of moderation by shouting it down as censorship.
Rejecting a cell microbiology paper from a computer science journal is not an attempt to suppress the paper. If anything, it is of benefit to the paper, since publishing it in the correct journal will increase it's visibility to the relevant audiences.
In contrast, content moderation, particularly in political subreddits is often motivated by tribalism and a desire to suppress particular viewpoints. It's true that these people could just go to another subreddit, but by the same logic reporters in Russia could just go to another country.
The effect of this type of moderation is that it creates tribes or "communities" of people who have similar opinions and never encounter opposing viewpoints.
Moderating based on topic is different than censorship based on viewpoint. If an argument is allowed but it's counterargument is not, that's censorship, not moderation.