Public Administration has to do with government agencies.

Businesses exist to generate income for their investors, and have no obligations to their employees other than to avoid putting them in danger. - A business can fire an unproductive employee, or replace a productive one with a cheaper foreign replacement

A public administration exists to provide safety and security to all citizens, and a public administration is not meant to be run for the interests of a moneyed few. - A government can not expel a citizen based on their "productivity" or "cost"