GFCO (glutenfreecert.com) holds the manufacturer to whatever they self-declare (20ppm, 10ppm, 5ppm, etc and even undetectable).

GFCO certifies individual products with testing.

GFCP certifies facilities with required systems and processes. These folks basically do the certification at a higher place in the chain and is where the industry is headed.

Definitely no barley, because barley is just as much a gluten containing grain as wheat.

Barley, rye, wheat and other grains each have their own protein. For those they are hordein, secalin, and gliadin, and they are all considered gluten.