I've been keeping butterfly koi for many years. there are some that don't consider them koi, IMO this is the big time show people, those of us that keep water gardens seem to like them very much, honestly I think they are far better than standard koi with plants and in most cases don't get quite as large as standard koi. Butterfly Koi and long fin koi are the same thing, however, hirenga koi are more true koi and are japanese breed long fins, Most are Hi Utsuri that have been appearing the last few years. I too have noticed distinct fin differences, actually three types for sure, One is a smooth rounded fin, one long and flowing with tips that come to a distinct point and one that is long but not as long as the pointed fin and has the shredded edges. My large Chagoi is this way and at night it is one of the best looking but during the day it's so dark it's hard to see and you can't see the detail in the fins. For the question about fins growing back, splits, and tears. and chunks will heal. But if fungus eats down all the way to the base it's a hit and miss, I have one that got a bad sore from a heron bite and it never grew back but it is almost not noticeable. I have a Hi Doitsu that had a turtle take a bite out of a fin before I remove the turtle out of the pond. It took two year to heal but now you can't tell it was ever damaged.