The difference is in the cryptographic key used to sign/encrypt the packages. The full definition should be "packages signed with fake keys" or "fake signed packages", but it's usually abbreviated to "fake packages".
Following with the wonderful explanation, this is why a game has first to be dumped decrypted then fake signed. We don't get to know what was the original signature, but it's not like it matters much as you can dump the game decrypted if it's running in the system.
Of course, that last requirement makes impossible to dump newer games on newer firmwares due to lack of public exploits and also to run newer games on current exploited systems due to firmware version limitations (Not only the versioning, actual code changes required).