There are a number of ways of paying employees and each have their advantages and differences. In regards to minimum wage employees, each state may have different regulations regarding how they are paid. For example, one state may require that they are paid weekly in cash, etc.
Hourly Payment - Paying an individual on an hourly basis is usually done when an employee does not work a set number of hours per week. Unlike with a salary, a company does not have a fixed amount that they pay the employee. They only pay for the time worked. Also, in many cases, employees are paid on an hourly basis so the number of hours can be kept under 40 in order for a company to avoid having to pay benefits to the individual.
Salary - Paying an employee a salary is usually done for higher level jobs where the hours may fluctuate. The company knows ahead of time exactly how much is owes the employee and even if the employee has to work more hours, the company does not have to pay more. With a salary, companies generally have to pay benefits if the employee works the equivalent of a full-time basis. The downside is that if there is an issue with the business or the employee cannot work the normal number of hours, the company still has to pay the employees the set amount.
Commission, quota, and bonus along with benefits provided are also other methods of providing compensation.