The first commercial hard drive was put on the market by IBM in 1956. Made up of 50 24" metal discs, it held a whopping five megabytes. By 1973, capacity was up to 30 MB with the revolutionary "Winchester" 3340. However, it was still a large metal disc.
At the same time, IBM was developing cheaper magnetic media in the form of the "floppy" drive. A sort of coated plastic, the cheaper, removable ( the "Winchester" was sealed ) medium was, well, floppy. The discs also didn't weigh several pounds or hold several MB. As they decreased in size from 8" to 5.25", they somehow got the name "diskettes".
Of course, modern hard drive platters are much smaller than either the 70's monstrosities or the "diskettes" of the day. Sometimes they're "disks" (short for diskette) sometimes they're "discs" (short for discus). I'm on the "disc" side of the argument, myself. Modern hard drives use sealed discs with heads that float on a cushion of air, just like the IBM "Winchester." They're obviously not descended from diskettes.
By the way, there's no argument over CD's; "Compact Disc" is a registered trademark.