That's interesting. So what you have is some sort of similarity metric that is colour based. You could define it as being 1 for an exact match, and 0 for not matching, so cyan, etc. would be 0 red, while orange may be slightly red (e.g. 0.1), and pink may be slightly more red (e.g. 0.25). This would be a 3D function/surface.
This would allow you to model classes of colours, like purples. Shades of a colour could then be any similar colour in the range 0 to 0.5 (or 0.25).
Yes, this is what Delta E in the CIELAB color space is meant for. But in RGB color space this concept doesn't make sense; well, only if you would accept a non linear similarity metric - but then what is the metric for, if you need to apply a curve to it to normalize it? But still, this is different from modeling 'shades' of a color (if we say 'shades' are varying brightness in RGB space using the 0.21/0.72/0.7 brightness conversion - but again, I argue that 'shades' is an ambiguous concept).
My point is, again, that colors are a much more difficult concept than some in this discussion are making it out to be, and 'distance between colors' is more complex still.
This would allow you to model classes of colours, like purples. Shades of a colour could then be any similar colour in the range 0 to 0.5 (or 0.25).