I think you may be combining the two ways of making a new key. I don't have a Punto and have not done this with Fiat keys, but I am an electronics engineer and have used these components professionally in a number of applications. Both have the same number so the car accepts both. They read the code in one key and make a 'clone' transponder. this is how Timpsons etc can make a copy without accessing the car.
Some transponders can be programmed with any number, after it is fitted to the key. To add a key to a car the list in the ECU is updated to include the new number. This is why you can't use a Fiat key on a VW). The number is nomally programmed at manufacture and is essentially random (it's a long number and some parts are the same and restricted to certain customers etc. The key transponder (apart from the latest types) just returns a number when interrogated. All the systems I know of program the car with a list of valid keys.
