I searched up what each character means, and it doesn't make sense. 兼 means twice or simultaneously and 职 means job. So does it mean second job? I understand that some people have a part-time and full time job, which fits the definition. What about students who only have a part-time job?
Students’ primary occupation is ‘student’ so a part-time job is a secondary occupation. So do housewives. Because most part-time jobs are secondary occupations so they are usually translated as 兼职.
If a person only has a part-time job which is his primary occupation, then translate part-time as 兼职 is not accurate for him. In this case, you can call it 半职 or 半职工作. A full-time job is 全职 or 全职工作. However, 半职 is not often used. Please use 兼职 whenever possible.
Legally speaking, in the US, full-time jobs are defined as 21 hours or more per week, and in China, 24 hours per week. This is officially called 全日制工作. And a job less than this amount of hours is called 非全日制工作.