The difference is that on those apps it would be a miracle if your "publicly" shared post were ever seen by more than a handful of strangers. None of those send it to the front page except in very rare circumstances (going viral).
The point is not the fanout factor but the lack of limitations. A public post is such that anyone can see, without authentication. A widely shared post that requires login to see is not public. An obscure pastebin paste is public, even though it's normally seen by a handful. But you don't get to control who these handful are.
A button that always shares content with the general public should be called "Publish".
(We'll discuss cache invalidation next time.)