Wow, I feel retarded. I was just talking to my cow-orker (definition: http://catb.org/jargon/html/C/cow-orker.html) about our tape backup system. He started talking about tapes and drives and such and I was trying to think about the big, fat tape library machine and where all those names fit into the puzzle. And then he said, "the machine has 4 drives" and I said, "you mean, there's 4 places inside the machine where the machine plops the tapes to read and write to?" and he said "yup."
It was then that I found enlightenment.
Tapes, floppy disks, cd-roms, and DVDs are all just plain old disks/media. Media that has no built in motor to spin or move the media, and no way to read and write to/from the media. However, a hard drive has all that stuff built in to the same device. Or at least modern ones do (I don't think the really ancient ones did).
So, is it correct to say "hard disk" or "hard drive"? Well, both! :-D Both terms are used interchangeably all the time since those devices have a disk AND a drive built into the same device. Actually HDD, a common abbreviation for a hard drive, stands for "hard disk drive", which is the correct term for them.
Now go, and teach others these valuable lessons! :-p