Chinchilla can be a color in several different breeds, but it also the name of 3 specific Breeds. (Giant Chinchilla, American Chinchilla and Standard Chinchilla).
(Edited to add: As accepted by the ARBA in the USA.)
My frenchie is chinchilla but I was curious to the fur type. His hair is very fine and harder to keep up with. There's rex fur, angora, etc, so I was curious if it was classified as a fur type as well.
I don't think it's a fur type, but I do agree that it seems harder to care for then the others. Flynn is a Chinchilla Holland Lop and her fur is WAY thicker then any of our other rabbits, she seems more at risk for matting in certain areas so I really need to watch her, particularily around her tail.
Their fur isn't nearly as thick as an actual chinchillas though. My chinchilla, Magyk, has probably some of the most beautiful fur I have ever seen on an animal, it's stunning.
On rabbits Rollback fur (common in lops) is longer and thicker. Rollback fur is fur that slowly goes back into place when rubbed from tail to head. I do think it's harder to take care of than my tans (they have flyback fur which is snappy and short).
So it's not necessarily the color but more so the breed or type of fur.