Is there such a type as a long haired corgi?

They do exist, but it happens randomly in litters (as I understand it) as a throwback to earlier breedings involving breeds that were used to create the current corgi.  Long hair is not part of the standard, so it should not be bred for intentionally.

They are called fluffies in Cardis. Fortunately the puppy farmers & backstreet breeders haven't jumped on the bandwagon in the UK & they are not promoted as "rare" or "valuable" either. They are no different to the dogs with a correct coat except for the coat & they are never bred from in Cardis

They can occur in Pembrokes too (throwbacks) but responsible breeders wouldn't ever breed from one, they aren't breed standard and are undesirable so shouldn't command any 'extra' in the price ;)

IME a Corgi coat is hard enough to keep matt free as the under coat is so thick, without the added problem of long hair......