It depends on the organization of the city government. It does not depend on the state. When a city is geographically subdivided into wards, as Chicago is, an alderman represents a particular ward. Other cities are not subdivided, and representatives to the city council are elected at large, generally in proportion to the city’s population. However, there is no legal distinction. The etymology of “alderman” goes back to the middle ages.
http://dictionary.reference.com/browse/alderman
I suspect it’s just a matter of local parlance.