Computer usage doesn’t determine that you spell it with a k.
A disk is indeed short for diskette, and disc is short for discus.
However, you can absolutely use a compact disc on a computer.
And while there are typically spinning platters or spinning magnetic strips inside hard drive disks or floppy disks, they are referred to by the whole unit as a logical disk drive that you’d see in computer.
If it’s possible to find them all now, you’d see that DVDs, CDs, Blu-ray, laserdisc, are all spelled like discus. 3.5, 4.5 floppy disks, hard drives, solid state drives, tape drives, etc all spell it disk.
So for the most part, being purely observational, you can see that anything shaped like a frisbee with a hole in it will be a disc, and everything else is a disk.
I think that’s slightly different than your explanation, as the terms are mutually exclusive.