(a) There shall be the following departments each of which shall be under the control and management of a board of commissioners that shall be the head of the department:
Fire
Fire and Police Pensions
Library
Los Angeles City Employees’ Retirement System
Police
Public Works
Recreation and Parks
(b) There shall be the following departments each of which shall be under the control and management of a chief administrative officer, who shall be the head of the department:
City Planning
Personnel
(c) The phrase “departments having control of their own special funds” and “departments which have control of definite revenue or funds” and other substantially equivalent terms used in the Charter shall mean the departments of Fire and Police Pensions, Los Angeles City Employees’ Retirement System, Library, Recreation and Parks, and the Proprietary Departments.