Final answer:
A system of government with elected officials managing city departments is known as a commission system. It is different from both the spoils system, where political allies are rewarded with jobs, and the mayor-council and council-manager systems, with their distinct divisions of elected officials and administrative roles.
Step-by-step explanation:
A system of government where multiple officials are elected to run various city departments is known as a commission system. In contrast, a spoils system refers to a practice where government jobs and contracts are awarded to political supporters of the winning party. The mayor-council system is a form of government where both the city council and the mayor are elected by voters, with the council handling legislative responsibilities and the mayor taking on executive functions. Lastly, in the council-manager system, the city council appoints a city manager to perform administrative duties.