So occasionally non-technical people would get confused by what is meant by "free software". To resolve the confusion some people called it FOSS or FLOSS, some people called it "Free as in speech" vs. "Free as in beer", some called it "Libre". But there is a meaningful distinction between locked-down proprietary software given away for $0.00 in furtherance of some ulterior commercial motive and software which is genuinely free for you to do whatever you want with it.
I think we need a similar distinction for the two meanings of "free speech". One which is the legal "Congress shall make no law..." narrow reading of the First Amendment and one which is the Voltaire style “I may not agree with what you have to say, but I will defend to the death your right to say it.” The first one is a law, the second is more of a moral value many feel is essential for a free society.
I think a lot of the problem is constitutional law running into Voltaire. You are correct that Twitter is not "censoring" in the sense that it's a private company not governed by the First Amendment. They are correct that Twitter is "censoring" content and is not providing freedom of speech for at least some users.