In the Vietnam era at least, the regulations required payment of a fixed amount per mile from your discharge station to your original enlistment or draft entry station. They did not give you a bus, train, or plane ticket. It was up to you to use the payment as you saw fit.
A similar practice was in effect when you were sent to another station within the US. You were not only given a fixed amount per mile from A to B, but also given a time allowance to get there. This allowance was only a few miles per day, probably a legacy from train travel. If you drove or took a plane to get there faster, the extra days were essentially paid leave.