As you guessed, airliner parking brakes are not like mechanical hand brakes on cars. (some small GA aircraft do have mechanical parking brakes, but most airliners don't). When airliner parking brakes are applied, hydraulic pressure presses the wheel brake packs from one end with hydraulic pistons, compressing the alternate 'layers' of friction material and metal/carbon discs together, preventing each braked wheel from turning.
When the system hydraulic line pressure fades away after the engines and electric pumps have stopped, pressure from the brake accumulator via a non return valve holds the parking brakes on. An hydraulic accumulator is a cylinder half filled with nitrogen gas under pressure, acting on a piston which separates the gas from the hydraulic fluid in the other half which is in turn is connected to the brake hydraulics via the non return valve and the parking brake valve. So the pressure of the compressed gas in the brake accumulator maintains pressure in the braking circuit of the hydraulic system - even with no pumps running. However, this pressure too eventually fades away, releasing pressure on the parking brakes, which is why all such aircraft have wheel chocks applied when they are not running.
After a period of standing, there may be no pressure left in the brake accumulator, so one of the tasks of the next pre-flight cockpit preparation is to check the brake pressure and run the electric hydraulic pump of the appropriate system if necessary to fully pressurise it again and recharge the brake accumulator. This is certainly what we do in Airbus FBW, I cannot remember now about Boeing 737 or other types.