There is no consensus on the difference between disc and disk, and in many contexts the two are used interchangeably. Disk is the standard spelling for computer-related terms such as hard disk and floppy disk. Disc is the standard spelling for phonograph records, albums (in the figurative sense—a group of songs presented in sequence), and components of plows and brake systems. But both spellings are commonly used for (1) CDs, DVDs, and other compact optical disks; (2) flat, plate-like bones; (3) flat, circular objects, and (4) disk-shaped celestial bodies. There are trends: disc is more common than disk for CDs, DVDs, etc. and plate-like bones, and disk is more common for disk-shaped things in outer space. But these trends are not so pronounced as to be conclusive.
Disk is indisputably the correct spelling for computer storage drives—for example:
If you must use a disk, there’s software that lets you use the optical drive on another network-connected computer. [Boston Globe]
It’s packed with features, including disk quotas to make sure none of your employees guzzles too much disk space. [Telegraph]
And disc is preferred for music records, albums, and machine parts—for example:
As well as the gramophones, Mr Thorne’s collection includes phonographs and disc and cylinder recorders. [Daily Mail]
The disc was the first release under West’s new “long-term worldwide label agreement” for his imprint through Def Jam. [Los Angeles Times]
Braking is accomplished with four-wheel disc brakes, 11.4-inch ventilated discs in front and 12.1-inch in the rear. [Montreal Gazette]
Elsewhere, usage of disc and disk is chaotic, and there are no clear rules (and usage guides differ on the matter). Our guess is that disk will eventually supplant disc in all but the latter’s special uses, but we’ll have to wait and see.