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.

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.