Chamber pressure is a relative thing, and is sometimes measured in different units, depending on who is doing the measuring and what method they use. It's tough to accurately compare pressure measured in CUP (copper units of pressure) with PSI (pounds per square inch), and your best bet is to use pressure readings only as a comparison between loads that were measured and recorded by the same folks, and in the same units. In other words, comparing pressure readings found in a given reloading manual with pressure readings provided by an ammo manufacturer may not give a true picture of how those pressures relate - and the same is true of readings given in different units, even in the same manual (or other source).
Chamber pressure is generally measured in CUP or LUP (lead units of pressure), using the crusher method. In short, a hole is drilled into the chamber of a pressure barrel, and a crusher assembly is placed over that hole and sealed. Inside the assembly is a piston which, when a cartridge is fired in the chamber, is forced to move when the chamber pressure bleeds through the hole in the chamber. This force causes the piston to crush a slug of copper (or lead when measuring shotshell pressure) of known hardness and length. Pressure is quantified by measuring the length of the slug after it has been crushed and comparing that with recorded data tables.
Pressures expressed in CUP and in PSI are approximately the same, according to "The Encyclopedia of Modern Firearms." In my opinion, the word to remember here is "approximately."
Another method of pressure measurement uses an electronic transducer. A strain gauge is attached to the outside of the chamber portion of a barrel, and when a cartridge is fired it creates vibrations which are transmitted to recording instruments and are displayed on an oscilloscope. These pressures are recorded in PSIA (pounds per square inch absolute), and in some cases the resulting pressure readings can be thousands of pounds higher than CUP or PSI readings. This difference can cause a load measured in PSIA to appear to indicate unsafe pressures when in fact the load is perfectly safe.
All of this can make pressure readings confusing, to say the least. Pressure values given in a loading manual are meant for comparison purposes - for comparing the loads found within that manual - and should be used as such. In any case, the handloader should remember that the cartridge case itself is the wimpiest thing involved when a cartridge is fired in a strong, modern action, and excessive pressure will begin to show there first. Keep an eye on your brass, and if you see signs of excessive pressure (extreme primer flow and flattening, case head expansion, cracked or otherwise damaged cases, etc), stop shooting that load and back off your powder charge until the high-pressure indicators are gone.