Well, the terms noise and signal are often used interchangably. For one man a signal may be a signal, and for another it may be a noise.
In the case of astrophotography. Dark current is a signal, but it is also a noise, and it contains non-random pattern noise. The bias signal is a signal, but it's also a noise, and contains non-random pattern noise as well. Glows are a signal, but they are also a noise. Skyfog is a signal, but it's also a noise. Read noise is actually just a noise. There is a signal that produces it, however that signal never enters the image, only it's noise does (and that is the reason why the term must be squared before being added to other noise terms.)
Dark current has it's own random noise. A shot noise. It's the accumulation of electrons (discrete events) over time. So that shot noise follows a Poisson distribution. It's noise is the square root of the signal. So if you have 100e- dark current, then you have SQRT(100) or 10e- dark current noise. We can subtract the extra signal. That 100e- offset. However, it's noise, random variations from the expected additional 100e- offset, will combine with other noises. It's SQRT(random+random+random+...)...you can't know what it is, so you can't directly remove the noise.
Thermal glows are similar to dark current, and actually related to it. A glow is actually the result of non-uniform dark current rates across a sensor. Since dark current rate is relative to temperature, if something produces local heating in certain areas of the sensor, then the dark current will be higher in those areas. There can be other causes of glow as well. Differences in voltage response, due to the manufacturing and materials of the sensor. Those are usually fixed bias glows. Change in voltage from the voltage source of a column of pixels to the opposite end of that column can create a voltage gradient, resulting in a visible gradient in the bias signal. Such a glow can change, especially in a sensor that self calibrates the column (or row or even pixel) voltages when it's powered up. Unfiltered sources of infrared radiation can result in non-thermal glows (I think some other ASI cameras might actually suffer from this, given the ray-like nature of some parts of their glows.) Like dark current, these are all signals, the accumulation of electrons (discrete events) over time. So, they follow a Poisson distribution. The noise is the square root of the signal. So if you have localized pockets of 150-300e- glows, then you have SQRT(150) to SQRT(300) noise, but localized to those areas. We can subtract these localized extra signals. The 150-300e- offsets. However, their noise, random variations from the expected additional 150-300e- offset, will combine with other noises. It's SQRT(random+random+random+...)...you can't know what it is, so you can't directly remove the noises.
Skyfog is another signal that enters through the aperture. It can be fairly uniform across the field, or it may be non-uniform depending on where light pollution sources are and how large the field of view is. For a given exposure the flux is usually consistent for each pixel, but a pixel in one corner may acquire fewer photons than in another. So skyfog tends to present as a gradient. It also has photon shot noise, like dark current, like your object signal. This signal could be tens to thousands of electrons in size, depending on how much light pollution you have. As this is the accumulation of electrons in response to incident photons on the pixels (discrete events) over time, it follows a Poisson distribution. It's noise is the square root of the signal. We can model the gradient and subtract it from the image. Like other forms of noise, it's SQRT(SkyFog), it's random, so it will combine with other noises. It's SQRT(random+random+random+...)...you can't know what it is, so you can't directly remove the noise.
These are all signals, all of these signals we remove from the image. Either with calibration, as in the case of bais and dark current and glows. We subtract master bias and master dark frames to eliminate the offsets these extra signals add to our pixels. We model gradients ("background sky") in our images, and subtract those gradients to remove the offset light pollution adds to our pixels. So, we can call these signals "noise". They are unwanted artifacts. They interfere with and interrupt our desired signal. So noise is an apt description. But there are lower level mechanics in play, and when it comes to understanding what's actually going on, it helps to understand that even though these things are noise in relation to the signal we are actually interested in preserving, each of them in turn is a signal WITH a noise component, and that while these signals can be removed, their noises cannot be.
The only thing we can do with true noise...the random variations in pixel values...is to average them out.