Pipehead-
Most of the info given is correct. Look up the oklahoma dept. of labor website and you can get more details.
The state card is now required for structural work as well. You could test on 3", 6",or plate-any number of ways, multiple codes.
Your card would simply list the process:SMAW, FCAW etc. and position tested:3g, 6g etc.
The qualificaiton paper itself is the only document listing specifics-wall thickness, ranges qualified. The typical information provided on a qual. paper.
Your employer may have requirements-wall thickness,progression etc. It would be safer to check with the employer for specific requirements they may have other than just "6g". That "6g" state card is a bit generic. They may require you to retest anyways, maybe not-depends on the employer. Your card can have multiple processes and positions listed on it. I have students who have qualified with multiple processes and they add them to their card for no add'l charge. Griff is right, just gets you a shot at the companys test-usually.
There is also a list of appoved testing facilities on that site. I have one in Guthrie, but there are probably others closer to you.