my previous response to this was "distortion"
and the other answers are entertaining but SSLtech makes a good point and I'll follow up
You have the amplifier to speaker interface - great example - speakers are non-linear and reactive loads and will sound completely different with different amps while the amplifiers all may measure quite well and very similarly into a resistor. You can't make blanket claims as to which characteristics work best either. Some speakers do not like amps with high damping ratios. These might be those designed with passive crossovers that assume they are being fed from an amp with a transformered output - like my various pairs of 604's sound very pointy and bad when driven from a Crown Reference but they sound pretty okay (which is about as good as they can sound) when driven from a MC-2120 off the 16 ohm tap. The Crown measures a little better on the bench and can boil water MUCH faster than the McIntosh can*.
In many high damping ratio power amps, and true of many line amps as well is HOW the low output impedance is attained. So if you look at an amplifier open loop as having a "real" output impedance of some value and then after applying 60dB of negative feedback around the whole thing, from the output back, it might have a virtual output impedance that is nearly 1000 times lower you might think you have something that can drive a load. Not necessarily. If the load is purely resistive you're okay however if the load is reactive it can interact with the feedback and essentially make the output impedance of the amplifier 'dynamic' - and you have the headroom limitations that come with inability to simply drive and sink current as opposed to simply maintaining a voltage that reflects some accurate representation of the input - so some amplifiers quote amazingly high damping ratios (low output impedance relative to load), can swing a 180 volts or more peak to peak and explode if you connect them to an electrostatic speaker for example. Or to say it more simply - some loads will short out the feedback and others will resonate and add to it - this is all part of getting your poles and zeroes worked out and taking into account your load as part of the circuit.
When you connect one thing to another you should in some way look at the whole thing as one circuit and consider all the interactions.
Apply this to microphones and mic preamps, line amplifiers driving long lines and so on.
Passive components can play too. I LOVE the concept of passive preamps. It's almost like someone thought up a whole product category in order to justify the sale of insane cables. Let's say I have a source somewhere and an amplifier elsewhere and they want a level control in between - and let's say a direct connection with good but not insane cable sounds great but it's way too loud. Let's further stipulate that the source has a real output impedance of 1 ohm and the load presents a purely resistive load of 100kOhms. Now I want to impact the sound quality the least so I figure I want a passive level control because what could be better than a string of resistors set up as a divider that I can pick taps off of to feed into the amp - this would be a stepped attenuator. I'll put that next to my comfy chair and put my source nearby so I don't have to get up to change program material or level. Now I go out and buy a passive preamp and even pay $1000 extra for the really groovy tonewood box and knob. This is a 100kOhm stepped voltage divider (pot) made with vintage Corning NE-60 resistors and silver Litz wire and whatever else you can imagine is the most excellent stuff ever. I plug it all together and sit down for joy at a reasonable listening level and oh my - it's no longer crisp like fresh celery - it's all soft and spongy like three week old rum cake and I'm all sad. I call my audiophile friend over to advise - same one who turned my on to the passive preamp that can't possibly be the problem because it's passive and used the best individual components in the universe. He whips out a pair of Valhalla interconnects (MSRP $9500 for 5.5m) and we hook them up and … ohhhhh yeeeeesssssss - that's better - or at least it's different and at that price the difference must be better and so it goes - nothing a well designed voltage follower wouldn't fix but since that is active it must be bad and whatever… sorry I was starting to spew there.
distortion is "something has changed between A and B" which I did not ask for
color can be distortion if I don't like it or it can be color if I don't know it's distortion or doesn't sound to me like distortion "should" sound… because distortion is bad and color is indeterminate, like, sometimes color is good but all distortion is bad?
color is something has changed but I don't know how to quantify or describe it? I don't have the tools either in ear training are test and measurement equipment or the knowledge as to how to use it to be able to know for sure what is going on?
at the end of the day color is whatever you want it to be - but distortion is 'bad'
*boiling water - a tech tip - if you find yourself wanting to measure an amp into a load at couple hundred Watts but don't have big fat dummy load. Take an 1/4Watt resistor at the value you want to the load to be, a coffee cup, some clean water (distilled water is best) and a pair of alligator clips. Clips to both ends of the resistor and drop into the coffee cup filled with clean water - you can now test your amp. At some point the water at the surface of the resistor will boil wiggle the bubbles off and keep going. This works for a while - long enough to measure anyway.
have a nice day