That's a good question.
Casual employees get paid, as Peartie said, a casual loading which is usually a dollar more an hour (but sometimes rounded off to 20% more). They can also be fired on the spot and without notice.
Part-Time employees are not paid the casual loading but do get sick pay, annual leave, long-service leave (after 10 years) and a secure position with at least a minimum of 15 hours a fortnight. They can work up to 30 hours a week, or more if agreed upon. They also need to give two weeks notice if they decide to quit or are fired.