No, they really aren't related at all, except for both being part of the US. The similarity of names is more coincidence of Europeans mispronouncing the native names. Kansas is named after the Kansa tribe, who lived in the eastern portion of the state. The "S" at the end came from referring to a pluralization of multiple Kansa people. Arkansas is even worse, as that word comes from the name of the Quapaw people, who now live in Oklahoma, due to the Trail of Tears. So in reality the two states should be Kansa and Quapaw. Definitely not twins.