The military does not pay you for travel on leave. They pay you for direct travel from your old duty assignment to your next duty assignment. If you travel home on leave, any additional cost is out of your pocket.
For example, let's say that you went to technical school/A-school/AIT at Base X. You have orders to Base Y which is 1,500 miles from Base X. You elect to travel home on leave after leaving Base X, before reporting to your new assignment at Base Y. You buy an airline ticket to your home, and it costs you $800. Your home is 400 miles away from Base Y (the new base you're reporting to after your leave). From home, you drive your car to your new base.
Assuming you had no dependents moving with you, for this move, you would receive travel pay of $225. This is the distance from your old base to your next base, multiplied by 15 cents per mile (of course, you would also receive $91 per day per diem for each authorized travel day, that you used actually traveling to your final destination). The $800 that you spent for a ticket home has nothing to do with it. That was travel to go ON LEAVE, which is out of your pocket, not the military's.
So, what if you don't drive a car? Suppose you leave Base X, buy a ticket home for $800, then buy a ticket from home to Base Y for $300 (for a total expenditure of $1,100)? In that case, the military will pay you what it would have cost THEM to buy you an airline ticket directly from Base X to Base Y. Let's assume that they would have paid $900.00. In this case, you would be re-imbursed $900, out of your total $1,100 expenditure.
Privately Owned Vehicle Shipment. If you own a vehicle, and get an overseas assignment, the military will either ship the vehicle for you, or store it while you are away. Some assignments (such as most European bases) allow military members to bring their own Privately Owned Vehicles (POV) with them. If you are assigned to one of these locations, you can drive your POV to one of the many POV processing stations in the United States (you get mileage reimbursement -- see above), and the vehicle will be shipped to one of the processing stations in the area of your overseas assignment. When your vehicle arrives, you simply go to the overseas processing station, and pick it up.
Some locations don't allow the shipping of a POV (such as Japan), and others restrict POVs to certain ranks (such as Korea where you must be command-sponsored or in the rank of E-7 and above to own/operate a POV). In these cases, the military will store the POV for you for free while you are assigned overseas.
A relatively new change in the law allows a military member to ship his/her privately owned vehicle within the CONUS (Continental United States) at government expense, if there is a valid reason, such as the member's orders do not give them enough time to drive, or if the member is medically incapable of driving.
