I hear lots of people saying that they "use darks to remove the thermal noise" or that "bias frames remove read noise." No -- bias and darks can remove certain aspects of unwanted signal but not noise. Distinguishing between true noise and unwanted signal is clarifying IMO.
Actually this interpretation of "noise" and "signal" is where I depart from typical amateur write ups and instead stick to the usage more commonly found in professional astronomical and engineering literature. I often hear amateurs insist that "noise must be random" - but I don't know where that idea comes from - and I think it makes it very hard to talk about - and understand - why people do all this calibration stuff to make their images look better.
I'm aware that many amateur web sites and even some amateur books on ccd imaging will use that "random" interpretation of noise - but I don't place much value in that if it is at odds with textbooks and journal articles in the field. Even worse - it goes against what I consider to be common sense.
I could cite many examples but here are two:
"Fixed pattern noise is removed from images by a technique called flat fielding, where a computer adjusts pixel sensitivites to be equal." Photon Transfer, James Janesick, SPIE 2007.
That is a casual summary of flat fielding in a well-regarded graduate level text on imaging sensors that has no problem talking about the removal of fixed pattern noise.
Many texts on noise and statistics don't even bother defining what noise is - because it all depends on context. My example is, if you are on the couch watching "the game" and someone starts describing a chore you should do - the game is the signal and the voice is noise. If instead the game is boring and the voice is offering a beverage - the voice becomes signal and the game is noise. Nothing about randomness here - just a thing that you want is being obfuscated by a thing you don't want.
One text that I like is Probability, Statistical Optics, and Data Testing by Frieden, in which he does attempt to give "A Definition of Noise." To me, he sums it up nicely and in a way that applies directly to the removal of pattern noise:
"This is a definition of noise which also shows its arbitrariness: the received message that is independent of one set of events may be dependent upon and describe a different set. For the latter events, the messages are not noise and do contain finite information."
Later, he says:
"The concept of noise is always defined in a specific context. As a consequence, what is considered noise in one case may be considered "signal" in another. One man's weed is another man's wildflower."
So - why do you want to subtract a master dark? To reduce the noise in it - and that noise is Fixed Pattern Noise. Flats are applied to correct vignetting - but also to make the pixel response more uniform - and reduce the noise.
So - sure - you can reduce and even remove noise, and noise need not be random. That's why there are terms like "random noise" and "noise reduction." And that's why images look better after a dark subtraction.