Disc and disk are varient spellings of the same word that pre-exist computing. Disc is more common in British English, Disk more common in American English. But yeah since computing came along disk has also been used more for magnetic media (hard disk) while disc has been used more for optical media (compact disc). I wouldn't be surprised if this only happened because of how the CD was marketed and branded as a "compact disc" as a trademark while hard disks and floppy disks etc were more generic terms.
I am not sure, but my oldest child was looking at an English brochure for a trip to France and a asked me "what the heck is a dis-coth-a-cue? Discotheque. A Disco, a dance club. And yes disco-tek is spelled Discotheque in English.
At its root this was originally a British vs. American English thing. However, the spelling of "disc" with a C has been used specifically as the trade name of various brands including both the throwable and optical media varieties, which have since become genericized trademarks.
For the optical media side of things, the name was coined by Phillips while they were consorting with Sony to develop the standard and named it the "Compact Disc" to compliment their already existing "Compact Cassette" product. They developed an official logo for the format which spelled it "disc." That's been with us ever since.
Volumes of computer storage are now colloquially referred to as "disks" because A) a significant majority of the early computer development milieu in general happened in America where we, or at least IBM, spell it with a K, and B) for a very long time, that's exactly what they were. Tape and magnetic core memory and wire loop memory were all early developments that ultimately gave way to the longstanding popularity of magnetic platter/disk fixed storage... With some exception granted to tape, which hung around for a very long time but definitely was not a random access storage medium suitable for general purpose applications whereas disks were. It's probably pure happenstance that the dominant non-fixed computer storage media also wound up being disk shaped, namely the various sizes and types of floppy disks. Computers handle linear tape based storage and random access disk based storage very differently, and nowadays random access permanent storage still has the "disk" moniker stuck to it even though it's now likely to be solid state.
As a generalized descriptor of a flat circular object, either "disk" or "disc" is appropriate but which is preferred seems to be largely depending on which continent you're from. The root of the word is indeed the Greek "discus," as in the object yeeted across the playing field by Olympic contestants.
In most varieties of English, disk is the preferred spelling for magnetic media (hence floppy disk, hard disk, disk drive), whereas disc is preferred for optical media (hence compact disc, digital versatile disc, optical disc). For all other uses, disk is preferred in American English and acceptable in Canadian English, and disc otherwise.
Less commonly, disc is used for magnetic media (as in floppy disc and discette; similarly, disk is sometimes used for optical media, as in compact disk and optical disk.
They're all the same word at their core, evolving from the older Latin word. The difference just comes in how the words were used to describe either a computer related device, hard disk, floppy disk, or a sound carrying device, disc record, compact disc.
It's the same thing. The difference is origin. Disk is American. Disc is British. Usually the only time "disc" is used in the US, is to refer to something round. A CD could go either way, depending on the writer.
"The spelling disk and disc are used interchangeably except where trademarks preclude one usage, e.g., the Compact Disc logo. The choice of a particular form is frequently historical, as in IBM's usage of the disk form beginning in 1956 with the "IBM 350 disk storage unit". "
There’s been some movement over time but in general disk was used for pc because you had Hard Disk Drives. Then their counterpart the floppy diskette (disks).
Disc as a term was used for media like compact discs and subsequently digital video discs, etc. and then pc components allowing them to be read and then written to did exist for PC’s and, as such, had the disc moniker. But that’s because they were already “discs” branding wise.
USB thumb drives, being created as portable removable media for pc’s were a kind of solid state disk and so they use the k. Even NVME, being primarily storage for computing devices, can also colloquially be called “disks” but more and more people just refer to them as drives and I suspect those who refer to them as disks may do so out of older computer hardware habits and that utilities (fdisk, df, etc)call any such media a “disk”.