The purpose for certifying hobby rocket motors is to enforce standards on motor manufacturers and to help ensure the safety of the hobby. There are currently three organizations that certify hobby rocket motors:
NAR, Tripoli and CAR accept motors certified by the others so launches held under the auspices of any of these organizations allow motors certified by the other organizations to be flown.
NFPA 1125 Code for the Manufacture of Model Rocket and High Power Rocket Motors is the base document for the testing requirements for all hobby rocket motors.
The contents of the document is carefully protected against casual reading. (You must purchase it and then even reading it requires access rights on the document.) The license does not allow reproduction here, but there are some interesting tidbits from Chapter 8 (Testing and Certification) that are worth paraphrasing. (This is taken from the 2001 version; the 2006 version is currently in review.)
As you can see, there is much lattitude for variation between individual motors.