I see you are suffering the same confusion that I had years ago when I first came here, in all things "supercharger" or "turbocharger" related I would trust Shortround and timo. This is how I understand it, but would be happy to be corrected.
1, The engine block, whatever it is, has a maximum of boost that it can withstand above sea level atmospheric pressure. This is not a constant because for various reasons like heat build up and lubrication it has limits both short and long term.
2. At sea level, it is simply a question of how much boost over atmospheric pressure an engine can withstand and for how long, so you have "take of power" and "war emergency power", "maximum continuous power" etc.
3. As the altitude increases it becomes harder to keep the boost you want because the air is thinner to start with, since compressing air heats it up, if you put hot air and fuel in a combustion chamber it explodes before you want it to. To make a huge increase in the compression it must be done in two (or more) stages with cooling in between. On the Merlin they had a two stage supercharger with an intercooler between, on the P-47 and P-38 there was an exhaust driven first stage turbocharger with intercooling before the normal single stage supercharger driven by the engine. As with everything all these set ups have advantages and disadvantages.
4. in all this, along with advances in turbos and superchargers there were also advances in fuels that allowed more total compression in the cylinder without detonation (octane rating), and advances in materials, bearings and lubricants that allowed running engines with higher pressures for longer.
In short, its a bit complicated
