Can we use Neutral (N on the selector) instead of Park (P) when
parking on a flat surface?
Possibly. Others have delved into the details already, read the other answers.
However there is one important point that I have not seen brought up yet.
Regardless of the type of transmission, you should have two mechanisms stopping your car from moving while unattended. With an automatic transmission, put the gear selector in Park, and engage the parking brake. With a manual transmission, put the gear selector in first gear (or reverse, whichever is recommended in the owner's manual) and engage the parking brake.
The goal here is to have a failsafe: systems can and do fail. Let us say you park in neutral and engage the parking brake. Now if someone cuts the physical cable (parking brake works like a bicycle brake with a steel cable to engage the brakes, and usually only the rear ones) they can roll your car away to a chop shop1, roll it into another car for "fun," whatever they want while you are not around.
What if you use only the parking gear but not the parking brake? While rare, transmissions do fail. What if the parts responsible for stopping the transmission from moving cracked and broke? Your car could roll away due to gravity or thieves. Note that even a "flat surface" does not mean "level" and what appears level might not be.
By using both mechanisms together, you mitigate the risk of your vehicle moving without you intending it to. Both systems have to fail, and at roughly the same time.
There is a third mechanism for use on hills, which is actually coded into law in some jurisdictions: curbing your car's wheels.
What is the mechanical difference between Park and Neutral?
Park engages a parking pawl inside the transmission which prevents the transmission output shaft or shafts from moving more than a tiny bit (the little bit of give is why a car might lurch a few inches after parking on an incline). Other than that, park might be equivalent to neutral, or there could be another locking mechanism. Any differences are specific to the manufacturer and model of transmission.
1 There are ways to steer cars even without the key, such as when the manufacturer does not put a steering lock in the car to begin with.