I had always thought that ‘disk’ could be differentiated from ‘disc’ as a USA versus UK phenomenon, or as computer disk versus a disc disc, but it seems it’s more complicated than that.
There are actually two types of computer disk (disc) as well. In computer terms, ‘disk’ refers to the means to store data magnetically on some type of hardware, whereas ‘disc’ refers to the means to store data optically via software.
As said before, the spelling ‘disk’ is preferred in the USA, whereas ‘disc’ is preferred in the UK for all but computer ‘disks’.
To complicate matters further, computer companies elsewhere in the world besides the USA and UK favour the use of ‘disc’ rather than ‘disk’.
Both words refer to round flat objects, if that’s any help!