The difference is there can be 100s of twitters, and they require voluntary usage. There's only one government, and you are required to abide by their rules, so restrictions need to be placed on the government.
If twitter and the government work together (e.g. twitter banning people that disagree with the government to get favors or avoid punishments) then that should be treated in a similar lense as government action.
The problem, though, is that there is one ginormous twitter, and the other twitters are pretty much like fleas on an elephantine body. Or it can be Facebook. They deplatform you, and you and your business may as well not exist at all.
It becomes interesting if it turns out that there indeed exists a symbiosis between the US government and social media companies wherein the latter are compelled to do censorship laundering on behalf of the former, maybe in exchange of their balls being not so tight in the regulatory vise. After all, it’s not censorship if a private company does it, right? Right? (wink, wink)
If twitter and the government work together (e.g. twitter banning people that disagree with the government to get favors or avoid punishments) then that should be treated in a similar lense as government action.