it's hard to separate the concept of noise from the concept of distortion. maybe distortion is a type of noise.
noise as high end audiophiles use the term is a (1) relative thing, and (2) an artifact of non linear actions by circuits and transducers. it can also be an artifact of room acoustics as reflective hash. even non linear bass nodes are forms of noise. although we don't typically call low frequency distortion noise, it is the same type thing.
when viewed as a relative thing, noise is what is the gets reduced when clarity, vividness and dynamics are increased. so it's a component of the sound that overlays the musical information in the original media and signal path .....a sort of veiling. some noise is inherent in every format. there is alwys some noise; it's either more or less.
when viewed as non-linear distortion, it's hash, or grit, or congestion......when a circuit or transducer is not working optimally. if a stylus is not traveling in the groove absolutely tangentially then the non-linear part of the result is noise. if the amplifier over-drives the speaker driver the non-linearity is noise. if the A/C power has ripples or less than pristine components then power supplies will yield some noise as a result with the signal they produce.
this is just how I use the term and contexts I use it in. YMMV, just my 2 cents. I never took an engineering course, and am technically limited in knowledge. maybe there is a simpler, more elegant, comprehensive explanation.
is there 'good/desired' noise? or 'good/desired' distortion? I suppose there is. but likely that subject is a matter of preference.
Mike, I want to be fair as I know why you describe things the way you do. Your descriptions make sense when you only look at them as descriptions of the what you hear, not why you hear it. Once you start applying the same description to the electronics they no longer fit.
When you hear the music sounds "not linear" as a momentary aberration, like it tried but didn't make it... that isn't a function of linearity. An aberration is when what you hear sounds distorted from what you would know the original to be (or the like), but is not a product of voltage distortion (linearity) unless something is broken. They are two different things. What you're hearing most of the time is inadequacy in current delivery, which is a complex interaction from the source to the speaker, each able to cause you to hear a momentary "distortion", aka an aberration, in the listening experience. The thing is that actual distortion (linearity) is generally speaking very consistent, were as aberrations come and go with different moments of music.
I do think your mention of nodes and reflection are great examples of anoise (acoustical noise), btw. But 98% of the time no one is talking about that when they say noise (enoise).
A lot of enoise, depending on the frequency, can certainly reduce clarity, but isn't an artifact in any such way (unless something is broken). Other frequencies enhance the experience for many, making enoise a benefit. And you're right it's always there. It's easily explained fact that electricity on wires or in the air can only divide or multiply, never subtract or add (even when you can use + or - to get the same math equation result).
Can enoise cause aberrations? yes & no because it isn't momentary but could be seen as consistent aberration. It isn't an obvious thing in equipment that isn't broken. It's like Tom said, you don't know till it's gone. You gain some clarity you didn't really imagine possible. It isn't a momentary experience of aberration, but rather a consistent one so it doesn't really read obvious to most listeners.
So in general, no, all those different momentary things are not "noise" as being discussed here.
Enoise comes from many places, and it's a
deep subject. Generally speaking the AC from wall is a huge source, and your gear can feed some back into it. But it's also in the air... and so on.