Disc and disk are both variants of the English word for objects of a generally thin and cylindrical geometry.
[1] By the 20th century, the "k" spelling was more popular in the United States, while the "c" variant was preferred in the UK.
[2] In the 1950s, when the American company IBM pioneered the first hard disk drive storage devices, it used the "k" spelling.
In 1979, the Dutch company Philips, along with Sony, developed and trademarked the compact disc using the "c" spelling.
[4] The words disc and disk can appear frequently in medical journals and textbooks, especially those in ophthalmology and orthopedics, and thus style guides often foster consistency by giving rules for which contexts take which spelling.