No big secret here; whereas the green mango is a special type of mango, the green papaya is just a regular papaya that hasn't reached the orange-outside-and-in stage yet. Though westerners might think this is an unripe papaya not good for much, it's used extensively in Southeast Asian cuisine for dishes like som tam (a.k.a. green papaya salad or papaya pok pok). If memory serves me right, it's used in West African cooking too, though I can find no reference to this after a web search.
What I did turn up, however, were sites that claim that green papaya has amazing curative powers. For example, http://www.longevityformulas.com/papaya.html reports that green papaya "improves the digestive system, regulates the bowels, acts as a tissue cleanser, digestive balancer, and free radical scavenger." They say it can help balance the body's natural enzymes and act as an immune system booster. They assert that it's antibacterial, amoebicidal, anti-parasitical and antiviral, too. Holy moly! Elixir of health or what?
On the other hand, they admit at the bottom that this information is not proven, and is provided for educational (and I would add commercial) purposes only. Oh well. It makes great salad, and it might make me healthier too. Nothing to lose, much to gain!