Well, I personally don't think they do imply the same thing from a user's perspective.
* Google, Facebook, Twitter, ... have become so well-known brands comparing to the new Persona. Normal users could quickly get a sense of what "Sign in with Google/Facebook/Twitter/..." means, but not "Sign in with Persona" means.
* Persona is not a social network while other mentioned brands are or provide a sense of social network. A user might perceive "signing in with <your-favourite-social-network-provider>" as an act of making the site a part of the network; while with Persona it's totally different.
