@solderdude I would not be so strict as to say that amplifiers don't "sound" and only output electrical signals. Yes, that is technically correct. But I think that everybody understands the reality that in the end, we listen to amps through speakers or headphones.
In the end we listen to speakers in a room or headphones on one's head. Sure they are driven by amplifiers but you don't listen to amplifiers.
Amplifiers can (and some do) change the output response audibly. This can be caused by linear distortion (which can even be level dependent) or caused by a (too high for the load) output resistance or from various forms of non-linear distortion or power output may be insufficient above certain levels.
Usually these 'amplifiers' are purpose built to modify sound in certain way(s).
In most cases of half decent amplifiers the distortion is too low to be audible and frequency response is well outside the audible range.
In that case you don't listen to amplifiers nor can you 'hear' an amplifier.
If they produce the same electrical signal which is fed to these transducers, they will produce the same sound under otherwise unchanged boundary conditions (speakers, room, environmental noise, and so on). Therefore, I'm OK to say that amps can and often do "sound identical".
Agreed that this is so. Ampifiers don't 'sound' though nor (should) modify it.
My point is that even if 2 amplifiers measure/perform the same under an identical load a person could still be convinced they 'sound' differently because of many reasons.
This is what perception can do.
I think some of us have used say tone control/EQ/effects and while making slight adjustment of say bass, treble or some effect heard (perceived) a different 'sound' only to find out later the tone control or effect was not enabled and thus nothing changed but still heard a different 'sound'.
Or, play music during the day and play the same music later in the evening and while technically everything remained the same can still hear a different 'sound'.
So I am not disagreeing with you but am of the opinion that using the word 'sound' can be tricky as that is perception related.