Early BBC technicians differenciated between disks (in-house transcription records) and discs (the colloquial term for commercial gramophone records, or what the BBC dubbed CGRs).
Simply put, disks are any storage media which utilize electromagnetic platters to store data. They are susceptible to data loss when placed near magnets, and comprise the following family of storage media:
One reason for the distinction is perhaps that the compact disc was invented by Philips, a European company (hence using the British English spelling, disc), whereas the hard disk was invented by IBM, an American company (using the American English spelling, disk). The distinction is mostly found in hardware documentation and is rarely maintained in software documentation for users, where disk is almost always preferred in the interest of consistency.
Another reason, explained in more detail in the external link, is that the audio field typically uses disc, whereas computer circles prefer disk. The CD was originally used solely for its audio applications. After the rise of the CD, some audiophiles began calling phonograph records black discs.