RGB video cards (with very rare exceptions) use six (original VGA) or eight (most things since the early 90's) bit D/A converters. Since a "shade of grey" is composed of an equal intensity of all three color elements the number of shades of gray you get is limited to the granularity of the D/A converters, IE, 8 bit, IE, "256 greys". (Monochrome CRT monitors use a single intensity feed connected to one of the three converters, while a color monitor displaying greys, again, needs to lock all three D/As together.) In principle you could get more shades of grey if instead of feeding a grayscale monitor conventionally you combined the outputs of all three D/As via a resistor network (or some other method) but you'd have to write a custom driver to make a sensible grayscale palette out of it.
One thing I'm mildly curious about is how many greys the Powerbook 540-era can actually display. I have an old TFT-screen'ed 486 laptop that has a very pretty display but it actually only has a 12 bit interface, which means it's only really capable of doing 16 shades of grey. (It looks fine under most circumstances because the video controller does some interpolation to keep things from getting "washed out" but you can reveal the truth by writing an appropriate BASIC program.)