Is there a difference between "disc" and "disk" for naming digital storage media?

Yes, according to Wikipedia the dis-k version of the word has been used to refer to magnetic storage media since the 1950s when IBM (a US company) pioneered the first hard drive. Subsequently the advent of optical media from companies such as Philips (Who are Dutch and therefore used the European spelling) and Sony meant that the form dis-c was chosen.

Etymologically speaking both words are synonyms, with the only difference being that disc is more common in British English, whilst disk is more popular in American English.

Rhodri (see below) also notes that the persistence of the word disk (even in European usage) for a magnetic storage medium is in deference to its American roots at IBM.

I was on the ANSI committee that defined the 5 1/4 inch floppy specification (ANSI X3-B8) back around 1980. Even then, among all the existing manufacturers, there was no consensus about disk versus disc versus diskette.

So both "disk" and "disc" are correct.

As an aside, that was a pretty rockin' crew. That ANSI committee met three times a year, and always in some cool place, like Lake Tahoe, or New Orleans during Mardi Gras, so we could meet hard all day and party all night, entertaining each other on company expense accounts.