Management is first and foremost about making the best possible use of all the company's resources to achieve goals. Staying close and ensuring that everyone delivers high quality over time and works on the right tasks is critically important in leadership.
Ensuring that the "machinery" works and that rules and routines are followed is also an important task for a manager, but it does not necessarily ensure good results over time.
"Administration" and "management" quickly become synonyms if the ambitions are small and it is easy to continue operations as before