It is typically said that administration, management, and supervision are different in that they represent three parts of a hierarchy. The administration sets policy, management gives the orders to implement the policies, and supervision ensures that the policies are carried out effectively. This is generally true, though the functions do not have to all be held by different people. There will be jobs that require a person to carry out more than one of these roles.
Administrators are typically those who decide the direction of an organization. They decide what the goals of the organization will be. These are the policy-makers who are at the top of the organization.
The administration typically does not dictate the details of how these goals will be achieved. Instead, the administration delegates that to the management. Management is an executive function in that it dictates who policy goals are to be achieved. Therefore, management consists of setting out detailed plans for how to accomplish what administration has ordered.
Supervision is the most detail-oriented and the least policy-oriented of these three functions. Supervisors do not set policy. They simply take the orders given by management and ensure that the workers are carrying them out. They are the people who oversee the day-to-day operations to make sure that the workers are doing what the management wants them to do.