The hardware is called (E)IDE, the protocol is called ATA.
Or that's what I was told -- I think there's some historic
revisionism involved, too.

ATA is the interface and standards for the ANSI standards based disk
attachment. IDE "Integrated Drive Electronics" is a marketing name used
to cover all sorts of ST412 compatible-ish early interfaces that moved
the brains onto the disk. IDE doesn't really mean much but "brains on
disk", ATA is a real standard.