Urban District

Usually a municipality large enough to contain a prefectural-level capital city will be divided into a number of urban districts (shi xia qu). 

The individually named urban districts are like counties (xian) in that they may contain both types of townships (xiang and zhen), although the inner city ones are usually divided into streets (jie).  I think some contain all three, but it is very difficult to discover what the situation is for many cities (shi) and their urban disctricts, as sometimes the inner core urban districts are tightly demarcated around the built up area, while in other cases they are newly absorbed counties that contain a lot of rural towns and villages.