It's difficult to say without having more information. This back up drive - what size is i? You say that you have two terabytes that are unused. I am assuming that you are not using Time Machine to do the backups. If you are, eventually, it will fill up the drive and then erse the older backups when loading the newer ones. If you are manually backing up, as I do, then the backed up date will remain fairly steady in volume. If this is the case, you could erase and reformat the existing back up drive, create two partitions of appropriate size, recopy the back up data to one partition and then copy the "other" files to the other partition. That method would help you keep things organized and separate. Both can then appear on the desktop as two drives.
As to how to move the files over to the other drive, if they are in a folder, then merely copy (drag) the folder over to the external drive. It won't take long for that process to complete.