SAAMI MAX pressures for centerfire rifle cartridges can be found here:
https://saami.org/wp-content/upload...99.4-CFR-Approved-2015-12-14-Posting-Copy.pdf
Pressures are listed in more than one format, with definitions listed in the opening pages. For example, the SAAMI MAX pressure for .308 Win in fairly common use is 62,000 psi and is indicated on page 43/375 as "MAP", or "Maximum Average Pressure". The reloading manuals I own do not list pressures, but rather use predicted velocities for the START Load and MAX Load with various powders.
The predicted velocities listed for these loads in reloading manuals are based on a specific barrel length (typically 24"), and cartridge overall length (COAL - typically short enough to fit in a standard magazine for a given cartridge). Presumably, none of the listed loads should greatly exceed SAAMI MAX pressure, at least in theory. However, variance in chamber dimensions, case wall thickness (i.e. different brands of brass), COAL, and powder Lot-to-Lot burn rate, can all lead to different results being obtained than what is listed in the manual. That is why the recommendation should always be to start low and work up a load safely, in small increments.
The differences in predicted velocities at MAX load with various powders represent the effects of different burn rates and gas expansion on muzzle velocity. For example, using a powder that has a relatively fast burn rate for a given caliber in a rifle with a relatively long barrel may sometimes mean the powder will essentially be completely burned long before the bullet ever leaves the muzzle. Relatively fast powders with heavy bullets can also generate early pressure spikes as compared with a slightly slower burning powder. In such a scenario, it is not uncommon for the faster burning powder to generate lesser muzzle velocity, even though the peak pressure may be much higher, than a slightly slower burning powder that continues to burn and produce gas expansion until after the bullet has exited the bore.
One way I have always found useful for thinking about powder burn rates and their effect on pressure and velocity is the concept of "acceleration". You can ramp up the pressure for a given weight bullet very quickly with a relatively fast burning powder (i.e. high acceleration), but if it all burns up before the bullet exits the bore, the muzzle velocity might not end up as fast as with a slightly slower-burning powder that has less initial acceleration, but which continues to burn and produce gas expansion until after the bullet exits the bore, and so ultimately generates higher muzzle velocity.
The bottom line is that different powders are
expected to generate different muzzle velocities in a specific setup for a given bullet weight. This is normal behavior and the MAX loads reflected in the manuals for a given set of conditions should be for the highest expected velocity without going over MAX pressure. But to reiterate, there can sometimes be large differences between load parameters in different manuals. Because of the large number of independent variables involved, it is always best to start low and work up slowly.