1983/84 is the transition year for P -> PX. They were phased in gradually as the factory ran out of the old parts. The new "PX" scooters were called the "Arcobaleno series" to signify the new improvements. "Arcobaleno" means "rainbow", and you can spot them by their rainbow badge. My suspicion as to why they became "PX---E" is because they added the electronic ignition to the 125/150 engines. Previously, the 125/150 were called "P125/150X", so they stuck the "E" on the end, moved the "X" to the front of all the P-range names, and thus the "PX" was born.
"P" was the scooter model name
"E" means electronic ignition.
"X" meant it had turnsignals
"elestart" means electric start
With the introduction of the Arcobaleno series:
*electronic ignition was added to the 125/150 engines.
*the EFL gearing was introduced.
*the fuel gauge was added (and the "reserve"position on the petcock was dropped).
*the horncast and headset got more angular.
*the glovebox got larger.
*the front axle was increased to 20mm from 16mm
*the front drum brake was "improved" (or so I hear. it was still pretty cruddy)
*the centermat changed from rubber to plastic.
*the fender crest was widened and changed to plastic.
*the cowl locking mechanism was redesigned so the locking levers were under the seat, to discourage theft.
A couple years later, the electric start was added as an option. On all European models, autolube and/or a battery was an option, not standard. Eventually, the "Arcobaleno" name was dropped, and everything just became PX---E. Even later, the mirrors were moved to the top of the headset, the "E" was dropped, front disc was added, the horncast got more rounded and sported a square badge, and the speedometer and badging got a makeover. (the "Disc" and "Millenium Edition" series).