Hi Ted,
Here at our plant, I retest everyone that comes in the door applying for welding positions. Due to the hard time of proving welder continuity, I simply retest whether you are carrying papers or not. I would think that papers simply will help to get your foot in the door to gain a chance at testing though. I agree that the ole' qualification/certification water has been muddy and everyone seems to have there own definitions. This makes it hard even if you know the correct definitions of those terms, because you then second guess whether the person you are conversing with knows the correct definitions. I run into these conversations on a regular basis with trying to figure out what our contracts are actually asking for, due to the terminology. Sorry for the bit of rambling there.
Most certifications are only good and valid as long as you are employed by the employer that tested(qualified) and certified you. There are certifications that individuals can obtain through an AWS testing lab that will be valid to carry from place to place. However, like I said most places will have their own test(s) to make sure you are "qualified" to do their type of work, then they will write up a paper that says that they "certify" that you are qualified to do that type work with the given processes and positions and ranges of variables dictated by the test(s).
Hopefully, I didn't confuse those terms any further for you.
Good Luck with your pursuit of happiness in the welding field,
John Wright