Chinchilla Lanigeras are considered to be the more "domesticated" genus of chinchilla.
There isn't really all that much that seperates the Chinchilla Lanigera from the Chinchilla Chinchilla, with the main difference simply being the tail length, with Chinchilla Lanigeras tending to have longer tails than their cousins. Another difference would be that Chinchilla Lanigeras actually usually tend to be smaller than Chinchilla Chinchillas, as well as having differing body shapes, which is displayed in the diagram.