I believe that disk is American English whilst disc is English English. In the era of personal computers with removable disks, the spelling mostly came from the US computer industry and has taken hold in other parts of the Anglosphere.
Currently, most optical discs are popularly referred to as CDs, DVDs or Blu-Rays, so perhaps the distinction is moot.
No one has used a floppy-disk for decades, the 8-inch ones were certainly floppy, the 5.25 inch ones much less so and arguably didn't deserve the name. You might have been referring to a 3.5 inch diskette.
Athletes still throw a discus I think. Whether your car is equipped with disc-brakes or disk-brakes probably depends on where you purchased it.