The car 'stalled' means the car's engine abruptly stopped because of some mechanical or driver fault and the car came to a stop.
The car 'stopped' doesn't imply the engine has stopped. It only says the car halted for some reason - intentional or unintentional.
'Stalled' is better in your first sentence, because that is the word mostly used when you misuse the clutch and the car jerks to a stop. You could say 'stopped' but it is not near as precise a description.