There are four different kinds of fur, or coats, on rabbits.
Taken from the books
'The Essential Rabbit' & 'The Rabbit Handbook'
The long and fluffy Angora coat is often used for
spinning because of its warmth. Because it is used to
make clothing, the Angora coat is often referred to
as "wool". The fur stands away from the rabbit's
body, giving it a very fuzzy, hairy appearance.
Rex fur is shorter than standard fur and is cottony
and airy to the touch. It is much thicker than standard
fur, and stands upright instead of laying flat against
the rabbit's body. Rex fur also has a double coat.
Satin fur has fine, somewhat translucent hairshafts
which make it look silky and shiny. Satin coasts are
about the same length as standard fur coats, but are
distinguishable by their luster.
Standard rabbit fur is the coat that most people
imagine when they think about rabbits. It comes in two
layers, an overcoat and undercoat. Both layers are approximately
one inch in length. The undercoat is soft and insulates
the rabbit against cold temperatures.