They are both private property. Courts have ruled that the first amendment only applies to public space. And despite the public nature of the Internet, whatever site or app we use is probably going to be private property.
I think two issues are being conflated here.
TikTok is private property, just like most media outlets are. They have right of refusal of any content.
The first amendment applies to
government suppression of speech. I.e. the government cannot tell its citizens what they can publish or say (with some minor exceptions). This includes private companies like TikTok. This has already been tested in courts and struck down, and SCOTUS justices both liberal and conservative have already expressed skepticism in oral arguments.
The US government outright banning a private media outlet will not stand up in court unless there is a legitimate national security component. (There isn't.)