Long distance running vs. Walking abunch of miles everyday. Which of the two would have more of an effect on skinniness of the legs and also the thinness of the bones?

Well. Running will not be good for thin legs and if the bones are frail it may cause more harm than good. You want to do cardio, maybe use a stairmaster and do wieght bearing excercises that strengthen bone and increase muscle mass. Brisk walking is good for your heart and endurance but if you want real physcial change involving increased muscle tone, wt bearing will need to b involved. Gd luc.