Extention for Troy's answer
In the USA, student job and work permit is two different thing. Student job is the job which is reserved for students only. It is the local and/or federal government sponsor's program. Local government offer matching pay, which is the employer pay 50% and the local government pay 50%. Federal government offer employer tax cut. So, the employer who hire student worker only have to pay him/her 50% of the wage plus the federal tax write off benefit.
Employer need to hire student status with legal work permit in order to meet the government co-op requirements. Social Securit Number is required for the US citizens and/or legal US residents (green card) and possibly F1 visa for foreign students.
Part time or full time, it depends on which program the employers are participate in. In most case, the employer offer part time. Because employer need not to pay for their part time employee's benefit.
All countries may have the same rule that need the working permit to work . I used to work for the American company in Mexico, I have to pay for getting the mexican work permit in order to be legally work in that country. So, other countries may have the same rules. At last, work permit and student job is two different thing.
Note: All schools are participated in local and federal sponsor programs, it is more common that students are only familiar with the student jobs only offer at schools.