When one wants to park a manual transmission (MTX) vehicle, one puts it in neutral, and engages the emergency / parking brake. With an ATX vehicle, the practice I've learned is to put it in Park, and engage the parking brake.
But if I need to engage the parking brake, then what exactly is the purpose of selecting Park? What does selecting Park do and how does it differ from selecting neutral?
In an automatic transmission there is a ring with teeth on the output shaft of the transmission. When the transmission is shifted into park a lever called the parking pawl is lowered against the ring. If the parking pawl did not land squarely into an opening in the ring the car will roll slightly and there will be a usually an audible click. The parking pawl now holds the output shaft from turning.
Without the engine running an automatic transmission is effectively in neutral in any gear except park. Theoretically with park engaged also applying the parking brake is not necessary unless the car is on a big hill because the parking pawl has more than enough strength to hold the car from rolling. It is a good idea to exercise the parking brake on a car with an automatic so the system does not freeze up.
PS. In a manual it is suggested to place the car in first gear or reverse then engage the parking brake and for good measure curb the wheels. In the event that the parking brake fails (more common than the parking paw) the engine with the sub one gear ratio will hold the car. The good measure of curbing the wheels will roll the car into the curb in the case that the engine can't hold the car from rolling.
When you engage Park but do not engage the parking brake, the weight of the car is held by only the little parking pawl lever inside the transfer case, as opposed to the car's actual parking brake. When you start your engine the next time, you can feel an unpleasant "thunk" when you move the selector out of Park, if there was even a tiny unevenness to the pavement. This is because the little parking pawl is literally FORCED out of the lock, overcoming the weight of the car. It is always recommended to engage the parking brake first, to let car's weight rest on the brake, before moving the selector into Park. That way, the next time you start the engine and move the selector out of Park, there is no more "thunk" because the weight of the car is held by the parking brake, not by the little parking pawl. (Unless you release the parking brake first, without holding the brake pedal, before moving the selector into Park. In that case, you would actually feel the car move a little, its weight falling back onto the engaged parking pawl.)
After arriving, recommended to 1. Engage parking brake. 2. Move selector into Park. 3. Let go of the brake pedal. 4. Stop engine.
Before leaving, recommended to 1. Press the brake pedal. 2. Start engine. 3. Move selector into Drive (or Reverse). 4. Release parking brake.
There will never be that rough "thunk" moving out of Park when these steps are followed, because the car's weight will not rest on the parking pawl that locks the output shaft.
The ideas behind this article are sound, but perhaps not always explained the best way, which may be why some posters haven't understood it! When stopping in an auto, the correct procedure is:- Stop with the footbrake, engage handbrake (parking brake), select neutral, release footbrake (it's this that allows the car to "settle" and thus not apply subsequent pressure on the pawl), re-apply footbrake, engage park, release footbrake, switch off. The "thunk" isn't the problem, it's the wear and tear indicated by the "thunk" that's the problem.
The handbrake is not 100% reliable, it wears off and when its worn, it can slip on steep hills. It may also loose grip because of water or debris.
So as a backup/redundancy in manual transmission cars, drivers used to put their cars in gear in addition to the parking brake. If you are facing up the slope, you'd put the car in first gear or if you were facing down the slope, you'd put in reverse gear making it hard (not impossible) for the car to move with the slope.
Finally, there's a third level of redundancy by using the wheels (curb the wheels) which involves turning the steering in the opposite direction of where the curb is to the car if facing up the slope or same direction if facing down the slope. If the curb is on your right, turn the steering left. If the car starts rolling, it will roll on to the curb and it has to jump over it in order to move further.
When auto transmissions came around, there was no way to put the car in gear so the park gear was added which is not actually a gear. It can lock up the transmission to the same effect. There have been cases where the tab on the locking prowl sheers off under the forces so it can not be your only way of holding the car from rolling.
None of these systems are 100% reliable so you should decide on a case by case basis how much redundancy you want to implement. More severe the slope is, more you need. It should be in this order though:
Parking brake should be your primary system to use for holding the car. But if you think the slope is too steep or your brakes are weak at the moment, put the car in Park too. That's enough for 99% of the cases.
