The OED gives fleece as
the wooly covering of sheep or similar animals.
Fur is given as
the short, fine, soft hair of certain animals.
This is a distinction of texture and to some degree, of use and method of procurement (see the entries for the verbal uses of these words also.)
Fluff is
light, feathery, floculent stuff such as the downy paticles that
separate from dressed wool.
But it also has the meaning of
the soft fur of a rabbit or other animal.
I don't see any authority for using "fleece" as a term for a rabbit's fur. The suggestion is that fur requires the death of the animial, whereas fleece is taken from an animal without killing it. But there is also an interesting (unrelated) OED definition of "fleece" which is the meat taken from an American bison. So go figure.