The Darkroom Automation web site has an application note explaining how variable contrast paper works (and sometimes doesn't):
Contrary to common belief the various emulsions in VC paper all have the same intrinsic contrast. The only difference is that one emulsion has a green sensitizer added to it - it is the same sensitizer used for Orthochromatic (blue-green sensitive) film. This is very old technology, the addition of erythrosine dye to the emulsion to make it orthochromatic was discovered in the late 1800's. Dupont came up with the idea of 2-emulsion VC paper - called Varigam - in the late 30's.
The reason that a high contrast filter is magenta rather than green is that VC filters also pass red light. The addition of red results in more illumination when you are dodging and burning. Try putting a deep blue filter in the holder and then hold a cardboard dodging card under the lens -- it is very difficult to see just where in the image you are with the card. The original VC filters were green to blue in color, but user's didn't like them, and that's where the change to yellow to magenta filters originated. Color heads also use yellow & magenta, while VC cold light heads are stuck with green and blue.