Here's the way it was explained to me. Remember, however, that I am a 67 year-old guy with reasonably good technology skills, but those were developed before the electronics revolution. So, if I get a number wrong or a concept slightly skewed, I have an excuse.
The charger/converter does two things. It converts 110v shore power to 12v power to run things like lights, the electric sofa, the thermostat on the AC unit and many more. It also acts like a conventional battery charger, which uses 110v power to recharge batteries, such as the 12v house batteries in an RV.
The standard charge function in the Parallax converter/charger produces a constant rate of charge, probably 13.6 volts. If I understand what is said about the Progressive Dynamics unit, it does the same. There is a sensor of some sort that detects when the battery reaches full charge, and the charger is turned off. But, it stays at 13.6v until it is turned off. When the battery drains a little, the charger comes back on to bring the charge back up. But, it comes back on at 13.6v. This can put too much of a charge into the battery, "cooking" off the water in the cells and shortening the life. It is apparently also devastating to AGM or gel cell batteries.
The better solution is a 3-step charger. If I understand the concept correctly, what this does is start with an initial charge rate of 14.2 volts for faster recharging, then at some point (I think around 90% charge) drop back to 13.6 volts, then as the battery nears full charge, it drops back to 13.2 volts, which is described as a "float" rate, designed to keep the battery fully charged without "cooking" it. Apparently there are some 2-step units that start with 13.6v and cut back to the 13.2v float rate.
According to my research, with the Progressive Dynamics 9100 series, this is accomplished by adding a Charge Wizard, an additional piece of equipment that controls the charge and reduces the voltage when appropriate. Again according to what I have been reading, the newer PD 9200 series units have the Charge Wizard built in to them. I don't know if this is a 2-step or 3-step unit.
bestconverters.com is also offering the Ultra III charger/converter, which has the 3-step charge controller built-in, offers better filtering against electronic "noise" in the 12v side of the converter/charger, and bolts right in to the Parallax housing without much, if any, modification. It's difficult to decipher the bestconverters.com web site at times, but this unit appears to be built by Magnetek.
I had an extensive conversation with the owner of bestconverters.com last week, and this is the unit he recommends. While he sells others, including the PD unit, he did not mention them to me.
You are correct that all of this applies only when plugged in to shore power for extensive lengths of time. However, my LTV is plugged into shore power at all times unless I am actually driving it. I use it 4 nights a week on average, staying in it at the rural property I'm preparing and improving for our new house. I keep it stocked with food, etc. all the time, and keep it plugged in whether at the rural property or at home, running the fridge on gas only when driving from point to point.
I have some other questions about batteries and charging, but I think I'll start a new thread in the batteries section.