What is the difference between photon shot noise and salt and pepper noise?
photon shot noise follows a Poisson Distribution, which is essentially a shifted Normal Distribution. It is an electrical noise usually caused by charge surges. Salt and Pepper Noise is more due to digital conversion, and is usually modelled using a Fat-tailed distribution (which is essentially a shifted Normal Distribution). What to note is for any unaltered image, the order of magnitude of each type of noise, with photon shot noise usually much lower than salt and pepper noise (unless specifically created)

True both noise can be treated using median filter, and often people use salt and pepper noise to represent shot noise.