It is certainly different, that's why I was drawing a distinction between hard and soft censorship. No hard censorship in the US, but the soft censorship is maybe more pervasive then you first realize. E.g. I think of the MPAA as a form of soft censorship, and one whose rating system was constrained at times by fairly conservative groups. Are there ways around it, yes, especially today, but not not as much historically. Major media coverage in the US also practices a soft censorship of attention and depth of coverage of certain topics too.

In America speech is censored by American private companies all the time. Racial or anti-semitic speech is often censored thanks for pressure from civil rights groups (i.e. https://www.nbcnews.com/tech/tech-news/facebook-bans-white-n...) and from lawsuits (i.e. https://www.bbc.com/news/technology-47705904)

Twitter has even begun censoring political speech from public figures: "Twitter will now hide — but not remove — harmful tweets from public figures" (https://www.theverge.com/2019/6/27/18761132/twitter-donald-t...)