I posted this as you indicated you found the differences.
2002STW3 ApplianceLinc 2-way with ground pin.
2002SHL3 ApplianceLinc with ground pin.
The 2002STW3 model has a power line transmitter in it. It can report its on off status. if queried or if manually turned on or off.
You would see a difference between the two models if you looked. I believe the base model doesn't have a tuned transformer in it. Just a coupling choke in two of the normally positioned transformer pads.
They are supposed to remember their programmed X10 address unless it was reprogrammed or a factory reset set it to the default A1.
Maybe power supply. Caps come to mind or the Set button looks like it is pushed and the power cycle factory resets it.
Long shot. The EEPROM that has the X10 data in it along with the on or off status. Maybe finally getting close to its rated. Erase rewrite specification.
I will look at one of mine now in storage and see how it acts. 2001SHL two pin or a 2002SHL3 three pin.
As expected. My programmed 2002SHL3 remembered its X10 address and On state. After a power cycle of maybe a 30 minute not powered period.