Here's my summary of what I read. Both words are derived from the Latin word discus, but throughout the centuries, the spelling of the word has changed between disk and disc. There are also some differences in usage between Britain and the US, and in most cases, you probably won't be confusing anyone if you use the words interchangeably. However, if you are talking to someone at Apple or others in the computer world, disc is used for material that is read optically (CD-ROMs and DVDs) and disk is used for material that is read magnetically (hard drives, floppy disks). Wham-O says that Frisbees are flying discs and car brakes are disc brakes. And the list goes on.
Got it? Quick. Tell me is the Milky Way a big spinning disk or disc.
Maybe the pictures below will help with Disk vs. Disc confusion.
First we have the disks--a floppy disk and a hard disk in an external drive. These use magnetic storage.
Next we have the discs--CD-ROM and DVD. These use optical storage.
But let's think about this a little more.
If disks have magnetic
storage and can be square or rectangular shaped, does that mean a
VHS tape that uses magnetic storage is a disk? 
Or because VHS tapes contain movies, does that mean they are discs like DVDs that have movies?
Then there's the flying disc.
Let's think some more.
If flat round things are called discs like the (generic) Frisbee, then are other flat round things called discs like a disc of peppermint candy?
And if a peppermint candy is a disc, does that mean that other sweet round things are discs? Or if they are square (i.e. Jolly Ranchers) like a floppy disk are they disks?
In conclusion, I am so confused.
