Final answer:
Municipal governments are the type of local government that manage communities larger than villages but smaller than cities, providing various services and operating under authority from the state.
Step-by-step explanation:
The type of local government that controls communities which are larger than villages but smaller than cities is known as a municipality. Municipal governments are responsible for a range of services including law enforcement, public transportation, and fire protection.
These governments can operate based on different models, such as a mayor-council system or a council-manager system. A key point to remember is that the authority of municipalities is granted by the state in which they are located.