Twitter didn't even censor the president, they just added a link below some lies he posted. He's been breaking their TOS habitually for some time and rather than ban him as they would anyone else, they made a special public TOS-exception for "newsworthy" bigwig public figures like him in their rules. The president gets to tweet things that would get you, a non-president, quickly banned from Twitter.[1] He's explicitly whitelisted as exempt from Twitter's usual control over twitter.com.
Now, the federal government is going to actually censor Twitter on his order, simply because they had the audacity to amend information to tweets from an account that they declined to suspend out of courtesy despite it breaking their rules for years.
[1]: https://www.washingtonpost.com/news/the-intersect/wp/2018/01...