Now I understand the picture. Your Disk Management image is truly worth a thousand words!
Yes, Disc0 is your SSD, with the MS reserved 100Mb partition first, then your C: system drive volume taking up the remainder of the disk.
The piece that doesn't fit together, is that Disk1 (Samsung HD501?) is properly recognized by Disk Management, is a 500GB disk set up as a Basic Drive, with the standard MBR 4 Partition structure, with 2 Partitions, that are both healthy. They both have a "friendly name" and a drive letter assignment. The Blue Band above them means they are Primary Partitions.
I am assuming the HP 475GB NTFS partition had your Win-8 OS on it, along with data, and the Factory Image Partition is the HP Restore Partition, which was used by clicking a special key combination, to restore the first Partition back to the Vista Factory New configuration.
All depends on what you want to do with the older HDD. Theoretically you should be able to check the file structure of Drive E:, and if intact, copy over personal data that may be on the drive. If the file structure has been corrupted by the upgrade or restore, you could download one of the data recovery applications (Aeseus Data Recovery Wizard - home edition freeware) or (TenorShare Data Recovery - free 30 fay trial) to copy off your data. Usually the 1st GB is free but need to buy the product for more data. Here are the websites:
http://www.easeus.com/datarecoverywizard/
http://www.any-data-recovery.com/product/
If you just want to use the old HDD as a secondary drive for data storage, in Disk Management you should be able to right click on each of the Disk1 volumes, to delete them separately, then reformat the drive with NTFS (standard allocation units) into 1 or more separate Primary volumes. Since it is listed as having healthy volumes, there should be no problem. Remember when you delete a disk volume, or reformat a disk, you lose all data on the drive. If you do a Full Format, it will take a while but check all the sectors on the drive and mark out any bad sectors if any.
hope that's helpful