Pixels don't have to be square. They could be arranged in a way that would cause them to be hex-shaped for example, and that would be what you would see on your monitor- a honeycomb instead of a grid.
The individual "grains" are particles which are extremely small-- nanometer scale. What you see as grain is a random variation in density of developed particles, as viewed through the entire emulsion. It is a visual phenomenon, rather than a physical one, as it would be if it were actual clumps.