Why is it different? How is it different? The behavior and impact isn't, is it? Can you give us something more than "it's not the same" because this response isn't wholly convincing.
The problem is that Facebook isn't the size of a Starbucks. It isn't even the size of a city. It's the size of a hundred cities. There are more users of Facebook than citizens of the United States.
It's like saying the US Congress can't impose censorship because you can just go to the EU and speak there instead. And if the EU censors the same things then you can just start your own country on a ship in international waters.
And who is going to come to your ship, or even find out about it, if linking to it is prohibited in the places where people actually congregate?
There is no town square equivalent where people have to walk past and can see you on their way to Facebook.
ICANN may be the top-level administrator, but the actual domain registrars are normal private corporations like GoDaddy and Google. What makes Google's domain registration service public infrastructure but not their video sharing service?
The scale point the sibling commenter made also drives to the heart of the issue - we can agree that I should be free to ban whoever I want on my private forum, but Facebook exists at a completely different scale that makes a qualitative difference in their impact on speech and society. The practical effect of banning someone or some type of speech on my forum is negligible. The practical effect of banning someone or some type of speech on Facebook is enormous. By giving Facebook that power (which they technically have, even if they aren't using it much now), you are handing them incredible power, maybe more power than any organization has ever had in history.
That makes it protected under US free speech laws, because the authority to grant/deny a domain ultimately derives from a government mandate.
The ability to post random shit on Facebook does not derive from a government mandate, so therefore isn't covered by free speech laws.
This is, for example, what happened to the contemptible Daily Stormer. There is no practical difference between a major domain registrar like GoDaddy or Google and a social media website like Facebook in terms of speech, except that at least if Google Domains shuts you down you can hypothetically (unless they seize/freeze the domain, which they have done) move to another registrar and the process is "transparent" for your viewers relative to being banned from Facebook...at least until they all run you off, with the most notorious example being The Daily Stormer again.