Great post up above from Brad, the breakdown of different electrical noises was interesting and comments in general on feedback as a noise as well.The amounts of feedback and whether it is global is always something I look for in amps and definitely a less is more approach often seems to be a good one.
If you live in a constantly noisy environment and then have gear that is generally obviously noisy with hum or fan noises, or if you have horns at 100+ db sensitivity I suppose at some level your perception seems to give in and tend to filter and cancel out some of the components of this noise floor and it becomes a bit like very mild tinnitus where you try and manage and listen through by focus. What this requires of our brains and if this comes at a cost or teaches us how to focus better I have no idea really but generally desensitising is helpful to some degree if there was a hypersensitivity to these things in the first place but certainly too much desensitising comes at some cost.
The differences between noise and distortion can maybe also come down to more about definitions and context. In the end noises and distortions are only an issue if you don’t like them. If you view these things holistically both mask the true signal which for me is the performance rather than the recording. There are clearly going to be distortions all along the chain from recording through to replay and finally in the perception. Noises can occur anywhere along the chain and also be captured in the recording.
For me noise and distortion both mask signal. There are more audible levels of each and also levels where they are barely audible but still have significant bearing on how we perceive the true signal... the performance and the music.
I worry about them primarily out of concern for them masking the low level signals that are responsible for so much ambience retrieval and the carving of true 3d spaces and correct timbre of instruments etc.
Take an old (1950s) Jazz recording like the famous Kind of Blue and you will hear a significant amount of tape hiss on this recording...however, it doesn't affect the ability to hear very soft cymbal brush strokes, inflections in the horn playing etc. In fact, with really good systems it seems to exist on a plane outside the music itself, detached if you will. This is because this tape hiss is not correlated with the music so our perception of it is different and more interestingly to me we can hear BELOW this noise signals that are correlated to the music...our brains are amazing processors this way. Same thing with clicks and pops on a record.
I am worried about noise in my system more for issues where it is being intermodulated with the signal to create new signals, which are now distortions, that are modulated by the signal but are now related to outside influences AND the signal. These will be non-harmonic multiples and will most likely be rather unpleasant to hear even at very small levels.
It seems nearly universal that when one cleans up the power with a regenerator or a power cable the first thing people usually notice is "blacker" backgrounds but while music is playing not statically. RFI/EMI is insidious and seems to "dirty up" the electronics output. As I said, I have seen this firsthand in a more obvious manner on an oscilloscope of mass spectral traces. We had to do a lot of work to minimize these effects so that we had cleaner spectra. Now, this is in the high MHz to Ghz range but with intermodulation you can get a lot of "fuzz" on the signal possibly from this. Block this from entering your system and you will probably immediately get cleaner output from your gear.