First the difference between wages and rates. Wages is a Payment for labor or services rendered by a worker/employee, be it on hourly, daily, or weekly basis. But Rates is more of a pricing term to have a particular commodity or service. I would perceive the difference as wages are paid for services rendered by an employee who is on the company’s payroll, while Rates are paid for services provided by a third party. Mostly we discuss rates for independent or third party contractors (e.g - IT contractors)
Now, Minimum wage is the lowest possible salary/ rate that an employer is allowed to pay their employees. This wage rate is determined by law so that the workers are not exploited of cheap or inexpensive labor. In India, The minimum wage concept is only for blue collard jobs not for white collard professionals.