The usual English spelling of consonant + C/K sound is with a K: rank, rink, sunk; mark, lurk, work; rack, pick; mask, tusk, risk; etc etc.
So disk would be the natural way of writing it if it were an ordinary import into English.
-sc is used in only a few Latinate words: mollusc, fisc, and subfusc are the only other three I know; and of course in US it's mollusk.
I don't know why disk was changed to disc, or when, or what influence. Probably French influence, I suppose. However, at some point disc became established as the British spelling. (Meaning: any round thing; this is long before computers.)
Computing usages generally come from America, so the spellings program and disk are now established, and I (and I think British usage in the main) contrast television programmes with computer programs.
The Compact Disc was invented by the Dutch company Philips, so they used the British spelling, and as it's actually a proprietary term I think you'll find all compact discs are so marked and spelt.
It becomes rather confusing now that compact discs are used for computer storage, just as floppy disks and hard disks are.
