When it's the government, is easy to say that censorship is when the government goes beyond time/place/manner restrictions on free speech.
But with the migration of the public commons to private areas, is it censorship to prevent a Black Lives Matter protest at the Mall of the Americas? Occupy Wall Street managed to survive so long because Zuccotti Park was on a privately owned public space which was required to stay open 24 hours a day, and thus avoid city curfews in public parks.
It's even less clear that a private entity like St. Martin’s Press must never change their mind about publishing a book, should they decide that doing so will give a Holocaust denialist the ability to use their name in support of his cause.
When HN users flag a spam comment for maid services in London, and it's later deleted, is that censorship?
We know all know of HN posts which cry out censorship for receiving downvotes.
The few times I've looked into one of these controversies, it seems more like people are using "censorship" as synonymous for "criticism I don't like." (Certainly not all cases! Just a boringly common majority of them.)
It's also a massive problem with the internet in general. After all, the internet doesn't have public property, ever. Every site is privately owned, so theoretically every site can choose what to allow. But without a public platform, that also means perfectly valid ideas can be basically banned from public view by way of large gatekeepers and popular communities banning them, regardless of their legality.
Either way, it's a tricky thing to answer, since any 'solution' wil cause a lot of problems in one case or another.
Censorship simply because you don't like what someone says has been around forever.