The difference comes in how these brakes work and the truck size that these brakes can handle.
Talking about Hydraulic Brakes, the power to hydraulic brakes is provided by the fluid. When a driver apply brakes, the brake pistons are forced to the wheel which happens because if the increased pressure of Hydraulic fluid. It is generally used in the trucks which weigh maximum till 33,000lbs. On the other hand, the Air brakes work on the air pressure rather than brake fluid. There are air tanks in the system which is pressurized when the driver presses the brake pedal. It helps in pushing the brake pads onto brake drums. Air brakes are used in much heavier trucks which are weighing more than 33,00lbs.
Also, the disc brakes are associated with hydraulic braking and brake drums are associated with air braking. The criterion of their functioning is completely different. The brake chamber plays a very important role in air braking as the air gets filled in there which pushes chamber diaphragm which results in braking. On the other hand, brake pistons play an important role in hydraulic braking which causes friction and thus braking.
If you want to know, what braking system is applicable in your car, you can check for the same in the car manual. If you don’t have your manual, you can always ask your dealers about the same. Also keep in mind that whenever you get your braking systems replaced in your car, don’t change the category of your braking system as it may spoil other components of braking as well. If you feel that something is wrong with your braking system, It is always advised to go to the dealer directly, and not apply your own mechanism as you cannot predict what is actually wrong in there.