But what is it? Do you not agree that if the waveform produced by
amplifier A perfectly matches the waveform produced by amplifier B, there
will be no difference in sound?

Of course. Unfortunately, they don't measure as accurately as you think they
do.

Yes they do. Today's modern test equipment is extremely precise. Much
more precise than our senses. It can introduce a virtually nonexistent
impedance (thank goodness for op amps) and has an error of measurement far
below what you think it is. The error is usually listed in the manual or
on the back of the machine itself.