Sanman, the color history of Apple is of particular interest to me. Here's what I've learned so far in my research.
The original Apple II from 1977 was a cheaply produced plastic mold that had to be hand finished and then painted. This went on until sometime in early 1980s when a new designer was brought in to deal with among other things the Apple II line while the other designers were busy with the Lisa, Macintosh and Apple III. It was then that the Apple II manufacturing process was updated and they were no longer hand finished.
Obviously there was your first change in color. Even if they tried to match the painted beige color, the III and IIe would not have been quite the same color as they used new ABS plastics and molds. I have no evidence that there was any effort to change the color scheme between them however. In fact they used the same brown keys with reverse white characters.
Based on comments from Frogdesign concerning the departure in color of the off-white IIc and general dislike of Apple's beige-color, it would seem the II, IIe, III and Lisa were intended to all be the same color of beige. Only differences in paint and plastic formulation resulted in slightly different shades. The Lisa in particular had a real problem of not only yellowing, but turning a nasty shade of orange, again more of an ABS formulation problem.
The Macintosh, we know was given a new shade of beige called PMS 453, for Pantone color reference. It had more brown content than a traditional yellow-tinted beige. So it was more of a light taupe than a true beige. That was done in part to mitigate the tendency of the Lisa to turn orange and yellowing in general but also to distance the Mac from the rest of the Apple family (albeit subtly). However, in general appearance it looks pretty similar, especially after a little yellowing. (Of particular interest to me are the Macintosh family advertisements of the era which can be found at MacMothership and Vectronics, where the Lisa and Mac are shown side by side in the same lighting. Maybe wishful thinking but there seems to be a clear difference in colour tint between them.)
Perhaps this is the "blue dye" addition that equill refers to, but I have actually never read that reference. However, that comment should not be construed to apply to Platinum which was a decidedly different color, not just a modification of Apple beige.
So, technically, the beige Macintosh IS a different color than the Apple II & II+, if for no other reason than those two were originally painted and produced in a completely different method than all other Apples. However, in general, the Mac beige has more brown than any other Apple. One other beige color exists during this time as well and that was the accent color which originated on the Apple IIc to co-ordinate with its off-white color and later on all cables until the change to Platinum. It is a slightly darker beige than the Mac, but very similar and referenced as "khaki". Despite the technical differences, the only thing I can say for sure is that the Macintosh was intended to be a different color and it is. The reality is that since the Apple II, III, Lisa and Mac lines were all run by different people and manufactured by different factories and considering how fractured Apple was at that time, there was probably no uniform coloration formula across all lines. That had to wait until Platinum, which was heatedly debated and carefully planned gray color scheme by Apple.