i have always found this was the simplest explanation

you have an engine and the manufacturer states it produces 100 horsepower in the handbook

this power is the power the engine makes

when you add an alternator to it and a power steering pump and an ac pulley etc this power is sapped from the engine power (parasitic losses) so you get brake horsepower

this way of measuring it's power is by bolting it to an engine dyno so the flywheel figures are what's being measured

if you add a gearbox to the equation and diffs and driveshafts, these deduct more power (transmission losses) and you get a smaller reading at the hubs (if you were using a hub dyno which bolts to the hubs)

then you lose more power (and accuracy) if you use a rolling road due to the tyres adding to the losses, this is then calculated back through the transmission to give you a best guess estimation of engine flywheel power

if you have the same car, tested on the same days with different mods this is the only realistic way to measure like for like on the rolling road

the problems in the other thread have occoured due to different interpretitions by some on the engine dyno side of things

engines produce heat, the rooms they are tested in need to have some sort of cooling, the cooler it is up to a point ehmore pwoer it will make, the more air flow it has the mroe pwoer it may make, etc, etc

the TUV bit is a set of standards that are set that mean that everyone and everything is equal when they are tested so you can compare like for like

one dyno was set up with these rules in place, others were not so you coulnd't directly relate one to the other
this same dyno was, in subsequent times, checked over to the same level as the TUV standards but for one omision, no one from TUV did the checks so it was not certified, even though the same checks were made to ensure it was at the same level (then it got technical and bitchy so i gave up)

so there you have it, unless you have the same paramiters for all your equipment across all the sites, you will never get a direct like for like comparision