Noise related to electro magnetic waves is called thermal noise. It have an simple voltage equation, Et = 2√(KTBRs).
This noise is also known as Johnsson noise or Nyqvist noise and the formula is often reformatted as temperature, current or resistive noise.
That is all there is to know about noise...almost.
Many experts have done their own noise definitions & expressions for special types of noise relative frequency/temperature/medium.
Two main types of expression are statistical distribution and power spectral density.
Many special cases of noise have their own names. Common names in RF-area are white noise, pink noise, dark current, gaussian noise, channel noise.
What differ these types of noise and respective mathematical model is easy to find on internet.
Diffusion noise (Ziel) and shot noise are mainly of interest when designing diodes and transistors.
NF (noise figure) is especially important to keep low at input stages for all analog sources (radio waves, sound waves, light, pressure..).
It is seldom the noise in it self that we are interested to know, it is resulting SNR & CNR that tells us in what amount noise is going to affect final signal.
In digital signal world do they have a similar signal quality-index, BER.
Most of these types of noises can be represented in several different ways in mathematical equations or statistical models.
Depending on type of noise can it be of more interest to describe it in linear or logarithmic(dB) and in time domain or frequency domain.
Information about these different kinds of noises and several more types are already described in other, easy to find forums.