I suspect it has something to do with the level of domestication, kind of like those gold-silver-bronze badges we've seen on pet yukkuris in the gutter_trash art. "A" might mean a very domesitcated yukkuri that's excellent for a pet (possibly bred for the purpose), while "C" might means a captured wild yukkuri and/or best suited for remirya chow.
Also probably affects the price. Mice and rats sold at pet stores as pets are much more expensive than those sold for you to feed to your pet corn snake.