The difference is coming when you are manipulating an image or a color (changing the brightness or the saturation of an image). This is most visible when lowering the saturation of yellow. Try it in Photoshop with RGB and with Lab mode. Do not switch to grayscale mode, because it is using luminance correction, but the saturation slider in the Adjustment>Hue/Saturation menu.
You can also see the difference when playing with my color picker (just scroll down to the full-blown example), which represents colors in the CIE Lch space (it is using CIE Lab in the background).