Your definition claims "a backup is a copy." The original claim was "a backup is a replication of the live dataset, although, usually out of sync to be useful

Your definition claims "a backup is a copy." The original claim was "a backup is a replication of the live dataset, although, usually out of sync to be useful when the main dataset goes bad." The only thing that makes a replica special is that it's in sync. Once you add the caveat that it's out of sync, it's just a copy.