"The PMBC Series ADJ – 12V looks like a good machine. But how close to the preset voltage does the unit get when charging? If it is set at 14.80 volts, does it end up at 14.80 volts?"
Not sure what is being asked, since Mex already knows what follows, but anyway----
The unit stays at the set 14.80 volts the whole time. (As set while not connected to a battery)
But when it is connected to the battery, the voltage on the connecting wires is lower, and rises as battery voltage rises with rising SOC.
Also once Absorption starts, the voltages seen at either end of the wires get closer together from the reducing voltage drop as amps taper.
At the end, in theory, with no amps flowing, the voltage on the wires would finally be 14.80 at each end. However, absorption never quite ends, but it could get to where it looks like 14.80 depending on the accuracy of the voltmeter.
I think that would be the same with any battery charger.