Dithering is the right term. It was called this even as far back as the Win 3.1 era where program installers typically showed you a full screen window with a background gradient that went from dark blue to black and used ordered dithering to make it look semi-respectable.

The threshold map of ordered dithering is still a source of noise, it just happens to be carefully pre-baked so that (original image + noise)==output makes the output more legible than what you'd get from just mapping the original image pixels to the nearest available color.

The error diffusion is static and baked into the thresholds chosen, but it's still there and choosing the error diffusion properly still matters to getting a reasonable output.