There are freshwater crayfish in Australia. the difference between a yabby and a freshwater cray is outlined below.
Freshwater crays have a harder shell and generally grow to a larger size. Depending on the species freshwater crays have short spines along the shell which make cracking them open to eat quite painful.
Murray Cray
Euastacus armatus (Family Parastacidae)
The Murray Cray (also called the Murray Lobster) is a large crustacean easily identified by its size (200 mm-300 mm) and its ornately spined body. They are active in the winter months especially in the more highly oxygenated waters of the Murrumbidgee and Murray. Breeding takes place in late autumn and early winter with the eggs being carried by the female until October. After hatching, the young remain attached to the female until they moult three times and develop the adult morphology (form). The Murray Cray prefers animal protein but is essentially an omnivorous scavenger.
http://www2.mdbc.gov.au/education/encyclopedia/wildlife/invertebrates/murray_cray.htm
Yabby
Cherax destructor (Family Parastacidae)
The Yabby is a widespread robust species. They are smooth-shelled, with a range of body colours from brown to the more typically blue with red appendage joints. They live in both temporary and permanent waters and can tolerate relatively high temperatures and low oxygen levels.
Yabbies are active in the warmer months and females may carry eggs from October to March. Adult yabbies average 100 mm -150 mm in length and may weigh around 100 grams. Yabbies generally feed on detritus but catch and eat any small animal that comes within range, including other yabbies.
http://www2.mdbc.gov.au/education/encyclopedia/wildlife/invertebrates/yabby.htm
Tasmanian freahwater giant crayfish grow to be quite a size however it is rare to see them this size in the wild anymore.
