A casual employee is employed to work as and when work is available, without any expectation of continued employment. A casual employee is not obliged to take a shift.
An employee is part time when there is an expectation of continued employment, and they generally work a set number of hours per week. A part time employee has made a commitment to work their shifts.
A restaurant employs a number of waiting staff. They work two or three days a week. These staff are part time, because there is an expectation of continued employment.
The same restaurant has a list of people they call upon if they are short staffed. These are casual employees, because it is the unexpected availability of work that determines their employment.
An orchard employs someone to pick apples for three weeks. This is a casual job, because the work is determined by the availability of apples to pick, and there is no expectation of continued employment.
An office employs someone to do the cleaning for an hour every Friday. This is a part time job, because there is always cleaning to be done.