In older days with smaller drives, less attention was paid to Partitions. But the truth is that Partitions have been part of the structure of HDD's for a LOOONNNGGG time. You may recall having heard of an old DOS utility called FDISK. It was a tool for creating Partitions on a HDD.
When you first get a new HDD unit it already has been "Low-Level Formatted" in the factory. That is the process of actually writing the basic magnetic tracks on the disk surfaces, dividing them up into Sectors with boundaries defined by magnetic signals, etc. Today's HDD units contain their own disk-level controller on their PC boards with a lot of capabilities and functions, too, and those are programmed at the factory also, including writing to their on-board memory a whole bunch of information specific to this one HDD unit. NOBODY can do a true Low-Level Format of a hard drive like this at home.
When you, the user, get the hard disk it is still useless for any operating system. The first thing necessary is to create one or more Partitions on it. A Partition is just one block of the disk space, all in a contiguous chunk, allocated to be used as one logical "drive". In many cases the first Partition created on a HDD actually is defined to use ALL of the available space, so to the user the physical unit and the logical drive are the same thing. But there is always the option to create a first Partition less than that, and later to use the remaining Unallocated Space to define more Partition(s). Now, when the first Primary Partition is created, two types of records are written to a specific place at the start of the disk. By convention, all OS's and BIOS's know to look at that specific address on the disk for those key pieces of info. They are the Partition Table and the MBR. The Partition Table simply contains the details of exactly what chunk of space is allocated to which Partition, as well as a few other details of its type and size. As more Partition(s) are created later, this table is updated. Thus any BIOS can find out exactly where any Partition on this disk is located, and exactly which one is supposed to contain the boot information and OS. The MBR is mainly a bit of machine code that is loaded by the BIOS into RAM and executed. It is a very low-level loader that simply uses the Partition Table data to find, load and execute the beginnings of the Operating system on the defined Boot Drive. But in fact, at this point there is no such boot info on any Partition - that info has yet to be added.
The second preparation step if to Format the drive (that is, the Partition). This does two things. Firstly, it installs on that Partition a File System with all its hidden special files that track the use of the drive's Sectors for file storage. The second is that you usually specify that the first Partition that you are now Formatting should be a Bootable drive with the OS's System Files installed on it in very specific locations within the drive's space block. These are the pieces that the MBR goes looking for in the Partition noted to be the Boot Partition, so that it can use them to load and execute the whole Operating System you install there.
Establishing a Partition and Formatting it can be done with many tools, including Windows' Disk Management. (Likewise, you can use such tools to Delete an existing Partition.) But it also is all done for you by the Install process that any Windows Installation Disk does. If you're starting with a completely blank new disk this is straightforward. But if you're trying to install to a disk that already has Partitions full of data on it, the Install routine will normally look for some Unallocated Space to use and not touch your valuable existing Partitions. You also have the option in these cases to tell the Install routine first to locate and Delete any old Partition of your choosing to create Unallocated Space for its new installation.
In some situations it is possible to Delete the first Primary Partition on a disk with more than one Partition. BUT this means you may be wiping out all the data in the Partition Table, and hence there is no record that the other Partitions even exist any more. If that is done, Partition Recovery software may be able to find all those structures and recreate a valid Partition Table for you. But if you did that first step and then proceeded to install a new OS (which will certainly Create a new Partition for itself), the Partition Table will have new data in it that may NOT include all the information necessary to define the other Partitions on the HDD. So they may exist but be garbled. MAYBE good Partition Recovery software can still figure this all out - I don't know. In your case, Windows disk Management tells you information that adds up to more space than physically exists, so obviously there is faulty data in the Partition Table. Furthermore, it appears more than one of the Partitions cannot be accessed, further demonstarting that the Partition Table data is corrupt. If Partition Recovery software can figure out the correct data for the Partition Table by examining all of the disk to determine its contents, maybe it can do this on your drive.
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