They are Pembroke Welsh Corgis with a non-traditional hair coat. They have a longer coat with feathering behind the ears, on their legs, tail and in the trousers. A fluffy may or may not have a double coat. Which ultimately means most fluffies shed less. I know this doesn't make since however this is our personal experience. To recognize a fluffy it might be helpful to know some historical background. Some think that far back in the history of the breed, the Welsh Collie might have been crossed in, and that is where the fluff gene comes from. It is a recessive gene and thus makes it very difficult to breed out.
Yes it is a serious coat fault for the Show Ring. However, there is no difference in personality from a Corgi with a smooth coat. They still have the same wonderful disposition and outgoing personality. They also can participate in all AKC events they are just not recommended for conformation. Let's not forget that the fluffy coat is not a health problem, it's nothing more than another coat variety that is not accepted in the Pembroke Welsh Corgi standards and will lead to a disqualification in the Show Ring.
Fluffies still have the same pedigree and are purebred dogs. Some people love fluffies and are looking for another because they are so adorable. Others don't like them at all. It's up to you to decide whether you like them or not.