There is some debate about whether it's 1000 or 1024

The SI units for these two multiples have been standardised. See, for instance: Prefixes for binary multiples. The 1000 multiple gets to keep the K, M, G prefixes (in line with existing physical units like metres and ohms that we are used to representing in terms of thousands).

For the 1024 multiple, the official term is binary: kilobinary, megabinary, yottabinary... abbreviated to KiB, MiB, GiB... YiB.

The real push for making the distinction didn't come from the disk drive world. The impetus came from the telecommunications field, where bitrates are commonly expressed in terms of thousand bits per second, not 1024. This is where the most confusion arose: telecom engineers talking to software developers didn't agree on what K meant.