If a digital image is underexposed, adding light post process makes image noise much more visible.
Digital photos don't have grain, they have noise.
With film, grain was the physical size of the silver halide particles that were sensitive to light. The higher the ISO of the film, the larger the particles were, making them more visible in the photo.
Digital noise is controlled by making sure the exposure is correct. Digital noise can be corrected to some extent by using de-noise software, but some detail is always lost. De-noising is one side of a coin, the other side of the coin is image sharpening.
Real World Image Sharpening with Adobe Photoshop, Camera Raw, and Lightroom (2nd Edition)
With film we exposed for the shadows and let the highlights take care of themselves.
Because of the way digital images work, we have to expose digital images for the highlights and let the shadows take care of themselves.
The concept even has an acronym, known as
ETTR - Expose-to-The-Right which refers to a digital images histogram. The histogram is a graphic representation of the luminosity distribution of the pixels in the image.
ETTR posits that we want as many pixels as possible on the right side (the most luminous side) of the histogram with few if any of them being all the way to the right.
ETTR
Learn Photography Concepts Look under the section: Qualities of Digital Photos
Photo Editing Tutorials Look under the section; Tones and Contrast.