As others have said and how I always see it:
- Discs are small, circular, flat objects, e.g. the discus;
- Disks are discs used for computer stuff, e.g. floppy disk(ettes), CD-ROMs, DVD-ROMs, hard disks, and so forth...
In other words, all disks are discs, but not all discs are disks.
Here's a shitty drawing I made to illustrate:
Ah.