Why is film grainy and digital noisy, and are they the same thing?

Film grain and digital noise look alike, and they share a root: light comes in packets. Film grain is the random texture of processed film. It develops from tiny particles of metallic silver, or dye clouds, formed from silver halide crystals that received enough photons. Image noise in general is random variation of brightness or colour, and it can come from film grain or from the unavoidable shot noise of an ideal photon detector: the randomness of counting individual photons, which is what a digital sensor shows as noise.

Shot noise is the easiest part to picture. Dim a laser pointer until only a handful of photons hit the wall each second, and the brightness flickers significantly, just as when you toss a coin only a few times. The relative fluctuations shrink as the reciprocal square root of the number of events. Collect four times as much light and the picture gets about twice as clean.

That explains the trade-off both worlds share. In film, larger silver halide crystals are more likely to receive the several photons needed to start development, so they give more sensitive film, for the price of being visibly grainier. Fine grain preserves detail but needs more light. In a digital camera the closest equivalent of a grain is a pixel, and like grain size, pixel size represents a compromise between resolution and sensitivity.

So grain and noise are cousins rather than twins: film grains are randomly distributed and vary in size, while sensor cells are the same size and arranged in a grid. Some video codecs, such as AV1, strip film grain out when encoding and recreate it on playback from a few parameters.