Yes indeed. It's only "censorship" when the government demands it. Engaging in voluntary moderation is not censorship in a meaningful sense. It is, in fact, an aspect of freedom of speech that people should not be compelled to engage in speech that they don't want to engage in.
Strictly speaking, you're correct -- but it also highlights that not all censorship is wrong or bad. It can very easily be a valid exercise of free speech rights.
Twitter (or any social media) moderating people's posts isn't wrong, for instance. Nobody's rights are being infringed when they do this. You might disagree with their moderation policies, but that's a different thing altogether.
Legally speaking in the US, it's only censorship when the government is doing it.
It's government censorship when the government is involved with funding the companies doing the censoring or when the FBI "nudges" companies to suppress stories. Having spooks in executive positions doesn't help the optics either. If anything, a bunch of companies acting in lock step to suppress certain stories or opinions should face anti-trust scrutiny...assuming we have a functioning justice system. The government outsourcing censorship to private corporations is government censorship...
Huh? It is now vastly more censored - everyone who isn't paying for the blue check is essentially shadowbanned, while "conversations" are dominated by ChatGPT reply bots and grifters.