i will use laymans terms (since i don't know the correct terminology anyway)
the pyro reads the heat being generated from the cylinders. the harder the engine works the more heat being expelled. climbing hills, towing, passing, bucking a head wind etc all cause the engine to work harder. since the pyro reads air instead of fluid it can respond extremely fast to changing characteristics of the engine, showing you what is happening inside the engine in REAL time and not delayed time.
the coolant temp reads the coolant, the coolant is heated by the castings around the coolant, the castings are heated by the combustion of the engine. the coolant temp can take minutes to react and register on the gauge. the pyro takes seconds.
by the time the coolant temp gauge reads the change in the engine temp the damage could already be accomplished.
i have seen the pyro read 1400F and the water temp not change. i have seen the water temp read in the red while the pyro is already back down to 600F. the two work completely independant of each other. you need both gauges to know what is happening.
hence, if you are to install just one, i recommend the pyro. it really changes how you operate a diesel. the myth is diesels LOVE TO LUG and nothing can be further from the truth. diesels generate tons of heat when lugging. diesels can expell heat easier and more completely if they are reving at a reasonable rpm.
if climbing a hill and the pyro climbs to an uncomfortable level then drop a gear, (speeding up the engine) and watch how fast the pyro drops back down.
and that, kids, is your leason for today.
cheers and peace.