There are supercharged engines and turbocharged.
Engine performance for a specific engine depends on rpm, fuel, air temperature at intake, pressure at intake, auxiliary devices it has to power besides the airscrew. We consider you dont change fuel during flight (other than maybe using additivas for WEP). On both, super- and turbocharged engines air pressure at intake is produced by the chargers of the engine, since most aircraft engines are charged. Air temperature is related to outside air temp, how much it is charged and how good the air cooler is (it heats up during compression). The engine has a max. possible pressure at intake, if you put in higher pressure the engine breaks.
So there is a max intake pressure which you can generate with the charger, it is much higher than the pressure that would be there without charger.
Turbocharged, the exhaust drives a turbine which compresses the air that is used to feed the engine. Since at higher altitude the air pressure is lower, the turbine which relys on the difference between pressure of exhaust and outside pressure works better. This is good because it has to compress the outside air more to keep the same pressure at engine intake. This makes turbo charged aircraft have a rather smooth performance.
In a supercharged engine the engine drives a charger directly, which costs some performance but needs a much smaller charger than turbo. The problem is that the supercharger delivers air pressure proportional to the outside airpressure, so it drops with altitude. This is counterd by using a "to big" supercharger and waisting excess pressure, so the charger can hold the max allowable pressure for the engine for some altitude. But above that the pressure drops since the charger can no longer deliver enough air to the engine. That is the point where you see the "zag" in the performance and the climb performance drops above this point, because engine power drops significantly.
Now this is counterd by 2 or 3 gear superchargers. Once the air pressure dropped enough that the next higher supercharger gear does not overpressure the engine you can shift up supercharger and get better performance then. AFAIK most WW2 planes that had multigear superchargers were shifted manually, so from a certain alt on the pilot was allowed to use a higher charger gear (mostly being no charger (n), first gear (1) and 2nd gear (2)). Not sure if some planes had automatic there.
Now with supercharger you get a zig-zag engine performance which leads to a zig-zag plane performance. On top you get less air resistance higher up and higher engine performance with colder air, which leads to curves in the zig-zag. Now depending on individual plane its either more curved or more sharp, also you can see 1 zag, 2 zag, 3 zag or no zag (Turbo). P47 no zags, Tempest 2 zags. Since the performance charts only show the relevant speeds they have all different scaling in x axis, which makes it look a bit strange sometimes.
(Sorry on accident wrote on wrong comp this wotp (wall of text post) is from schutt)