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.
Examples
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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.
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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.