Kerry volunteered to serve in Viet Nam. He served two tours, one on a ship in the Pacific in support of Viet Nam action, and an abbreviated one as a command of a Swift boat. He received five medals there, including three for injuries in the battlefield, though none of his injuries were life threatening or extremely serious. His second tour ended early because he'd been injured more times than was allowed. He's been attacked by a group of veterans with longstanding republican ties who say he lied about his own record to get the medals, and his lies helped them get their medals. All of their stories have been pretty thoroughly debunked.
Bush joined the Texas Air National Guard after his father got the Lieutenant Governor of Texas to get him in according to that Lieutenant Governor who is a long time Democrat and part of the Kerry campaign now. He was suspended from duty for making no attempt to meet his training certification. Afterward his superior officer was pressured to sugar-coat his review. Bush then transferred to Alabama, where the only record of his showing up for duty is a dental examination. After he finished his work in Alabama on a Senate campaign, he moved to Boston to get his MBA, and he never completed the remainder of his guard duty. He was later honorably discharged.