Correct, "Atmospheres" is a measurement of pressure equal to the measured air pressure at sea level.
PSI, likewise is a measurement of pressure.
1 ATM of pressure is equal to 14.696 PSI.
In physics, Volumes is not a measurement of pressure, but of volume (or amount).
Someone jump in if I end up muddling this next part....
As air is compressible, it's pressure is a combination of the amount of gas and the size of the space it is compressed to (temperature effects this as well).
An empty beer bottle, just sitting open is filled with 1 volume and thus its pressure at sea level is 14.696 PSI. Fill it with 2 volumes and its pressure is now 29.392 PSI.
That link that Akueck posted above shows volumes between 1.3 and 3.5. Giving pressures from 22.044 PSI to 51.436 PSI.
The thin screw top beer bottles in the US (edit
at the beer company that I work for /edit are tested to 100 PSI (not every one is tested though, just perhaps one in a hundred. So a safer target would be 50 PSI max pressure). I'm not sure how thick the bottles you purchased are, but it's good to know your upper limits.
Hopefully that helps and I didn't get anything wrong. One thing to remember is that I completely disregarded was the volume of liquid as it's non compressible and it's assumed that the gas is dissolved within it. Someone confirm this is correct?