Here are the basics and the way I understand it.
With a Legacy LNBF and Receiver, the signals from the LNBF are sent using 950 MHz - 1450 MHz. So if you were to put a splitter to send the signals to two receivers, they would both have to watch either Odd Transponders or Even Transponders; depending on which voltage (13V or 18V) was last sent to switch between Odd and Even, but could watch different channels.
However, if this single LNBF had two separate outputs so that it could feed two receivers, then each receiver could watch channels on Transponders with opposite polarity (Odd/Right Hand or Even/Left Hand). Dish calls such a (legacy) LNBF a (legacy) Dual (not a Twin), which picks up a single satellite, but feeds two receivers. Each output is still only using 950 - 1450 MHz and only one polarity at a time; just each output is independent of each other.
DishPro, not as good as fresh French Bread, but better than legacy. With DishPro the signals are bandstack so that the LNBF output is 950 - 1450 MHz for Odd Transponders, and 1650 - 2150 MHz for the Even Transponders. So now if you took 3 DishPro LNBF and feed a DP34, you only need 3 inputs to have all 6 signals, i.e., both Odd and Even transponders from 3 satellites.
So basically all the DP34 is doing is connecting each Receiver Port to a Satellite LNBF Input Port which contains both polarities for the single requested satellite. It will also allow (upto) 4 connected tuners/receivers to each access a single Satellite/LNBF Port at the same time, and/or different LNBF/Ports.
DishPro Plus, as good as fresh French Bread, but not as good as Gumbo and French Bread.
Basically the DPP44 does the same thing, it takes and connects a single receiver to a single LNBF port with both polarities available.
However, it will also connect a dual tuner receiver to 2 different LNBF Ports with both polarities from each, using a single cable. This is where the magic comes in.
I haven't figured out how it does this (yet), but I suspect when the DPP44 receives a certain command, it sends the requested signal for the second tuner down the same line by either offsetting the frequency, another bandstack, or multiplexing it. Then the DP Separator, separates it to the correct tuners. However, I'm sure these dual tuners play a part in converting this 2nd signal; if not, you would probably be able to take the outputs from a DP Separator and send it to separate receivers - which doesn't work.