Surely it depends on the context in which it/they are being used.
Identified is usually only mentioned ATC to ATC during a radar handover or ATC to AC when the ac is positively identifed by the controller using the proscribed identification techniques/methods.
Contact would be used when an ac had undergone a radar handover and the ac would be told to "Contact xxx radar 111.11" or when one ATC to another is referring to an ac and points said ac out using radar. As soon as the listening controller is happy he he has identified the subject ac he replies "contact" so both parties know the which ac they are referring.
Just read that through so not convinced it's that clear but I've never professed to be any good at this lark!