As far as I know there is no connection. Cotton is derived from the genus Gossypium, usually G.hirsutum or G.barbadense. Gossypium is a member of the Malvaceae family, whereas Jatropha is a member of the Euphobiaceae and so there is no real botanical connection.The only link between the two is a very tenuous one: there is a species of Jatropha called the "Cotton Leaf Jatropha", (Jatropha gossypiifolia); as you can see the species name here is similar to the genus name (Gossypium) of true cotton. However this link is only in the name and the species has no relation to the cotton plants of commerce. Check out the two www below for information about Cotton Leaf Jatropha and some pictures.