There is no disc controller on the motherboard with IDE drives.
That's what Integrated Drive Electronics means, after all. Turn
your disc unit over. See the chips and circuitry? That's where
the disc controller is. The motherboard contains merely a
PCI-to-ATA bridge.
Yes, yes, we all know that, [...]
Apparently not. M. Arno and M. Speed don't, it seems. It's
disappointing in the former case.
If you're going to be completely pedantic about it, and continue on
with the networking analogy, [...]
It's not a networking analogy. Things that connect computer buses are
known as bridges, bus bridges if there's scope for confusion with any
other sorts of bridges. There are many sorts, because many computer
buses have been connected together over the years, from Unibus to the
VESA Local Bus. In the world of PCI we have PCI-to-ISA bridges,
PCI-to-ATA bridges, PCI-to-PCI bridges, and of course the bridge between
PCI bus 0 and the processor bus.
In the case of an ATAPI device, [...]
In the case of an ATAPI device, the actual bus is still an ATA bus. The
bus itself isn't any different. (If it were, after all, one wouldn't be
able to correctly connect the device to the cable.) Nor is the
PCI-to-ATA bridge connecting it to the PCI bus any different. The
difference between ATA and ATAPI is in the disc unit itself, at the disc
unit command level and (to a lesser extent) the disc unit device
register level, not at the bus level. The bus is the same, and the
bridge is the same.