To elaborate a little. During the war, a "points" system was devised under which varying numbers of "points" were allotted for having met certain special conditions of service; such as overall service, overseas service, promotions, decorations and awards, wounds, campaign credits, etc. (In the case of wounds, the appropriate number of points was awarded for BOTH the incidence of being wounded AND the resultant Purple Heart award TOGETHER - not for both SEPERATELY (remember, this was long before JFK and LBJ, et al, made double-dipping routine procedure). When an individual accrued the requisite number of points he was eligible to rotate home, usually on individual orders. In the interest of fairness, when an entire unit rotated, "high-points" men ("Old Timers") were transferred in and those with lower "points" totals ("Rookies") were transferred out.
The unit listed on an individual's discharge/separation certificate is merely the unit to which he was assigned at the time of discharge/separation - in your Dad's case, Company K, 324th Infantry, 44th Infantry Division. The dates are sucha that he may well have returned with the division or returned on individual orders, being assigned to the division at Chaffee. He may have served overseas with Company K, another company, another regiment or even another division. Try the divisional association first. If that fails, you'll have to access official records.