Blood in the urine is a common side effect of kidney stones caused by the irritation produced by the stone against the delicate lining of the urinary tract. However, the intestines and urinary tract do not meet, so blood from a kidney stone would not find its way into the intestines, and thus the stool.
Bloody stool may be caused by internal or external hemorrhoids, anal fissure, colon polyps, diverticulitis, Crohn's disease, or gastric ulcer. Usually the brighter red the blood, the closer to the anus it is originating. You son needs to be seen by his doctor for both problems.