Where the master terminology comes in is that a certain version of ATA added bus mastering DMA from the drive. Maybe some harddisks had a jumper to disable or enable that
I don’t say this to justify sticking with the older terms, just to assert that they were actually used.
So you have IDE0, primary, and IDE1, secondary. For the four devices a typical system would support, they would be referred to as primary master, primary slave, secondary master and secondary slave. This was extremely accepted terminology.
Newer machines and BIOSes could usually boot from any of these four devices but originally, many machines could only boot the primary master. That's why it's the master and the other one is the slave -- it is subservient in the sense that it can not be a boot drive and was usually used for secondary storage, not OS.