Your second sentence is true: Private censorship isn't the same as public censorship; you have no fundamental right to free speech in a context owned by someon

Your second sentence is true: Private censorship isn't the same as public censorship; you have no fundamental right to free speech in a context owned by someone else (private website, physical business, physical home, etc.). But your first sentence needs adjustment: Free speech is something a government takes away from its citizens. It's a fundamental right held by everyone in the world. There are governments that fail to protect it, and of course many that actively violate it.