On an automatic car, what is the difference between P and N?

Park locks the transmission for all practical purposes, so you can't move the car without breaking or otherwise causing harm to the transmission. Neutral is the same on a manual or automatic car whereby you can coast in neutral and the car will roll unless you use the parking/emergency brake.

neutral just allows the vehicles to roll freely

park keeps the vehicles stationary. there will be some movement, but it will hold the vehicle so you can park it anywhere.

park is basically neutral, but a parking pin locks the transmission from moving. but the engine can still run without turning the wheels

that's why you could only start an automatic car in park or neutral.

"p" or park is the same as neutral but with the locking pin that stops the output shaft to stop the car from rolling. my advice for useing an auto is always stop the car with your foot on the brake, then pull the parking brake, then put the car in park so as to not strain the park pin on hills. if the car rolls a foot or too and then hits the park pin on a steep hill its a bit hard on it. if you have a manual it is best to have a healthy parking brake and always put the trany in a low gear 1st or reverse when parking. my cars park brake is weak so i chalk the wheels on hills to be sure it wont try and escape.

Park and Neutral do not do the same thing. When your car is in park you cannot manually move it. ie: push it. When it is in neutral you can move your car by pushing it or rolling down a hill.

I think that neutral just stops the power transmission to the output shaft of the transmission. Park does that plus engages a locking device, a pawl into the works

When a car is in neutral the rear tires spin or move freely or the car will roll if not on flat ground. When in park the car will not move.

you'll roll down a hill in neutral, in park the transmission will not allow the wheels to roll