EDIT: Seriously, this question was downvoted within two minutes? Why?
EDIT again: The best I've been able to come up with by reading the comments and docs is that they attempt to solve the same problem, but OpenID is based on the backend of the website you're logging into issuing a request to the auth server over HTTP, while Persona has the auth server issue a very-short-duration cert for a public key generated by the client.
EDIT: Seriously, this question was downvoted within two minutes? Why?
EDIT again: The best I've been able to come up with by reading the comments and docs is that they attempt to solve the same problem, but OpenID is based on the backend of the website you're logging into issuing a request to the auth server over HTTP, while Persona has the auth server issue a very-short-duration cert for a public key generated by the client.