In this item we won't deal with in-depth linguistics, but will rather deal with some terms that often get mixed up in one's head, especially for those who aren't experts in administrative divisions of all sorts. Some terms have been evolved in modern times, while some were derived from divisions which were conducted by different imperial dynasties.
Provinces 省 (shěng) - Currently there are 22 provinces in China (23 for those who include Taiwan), but altogether there are 34 province administrative level divisions, including 5 autonomous regions (自治区 zìzhìqū), where the minority group which dominates the region in terms of populations has some legislative power, 4 direct-controlled municipalities, 2 special administrative regions and on claimed province. Although some past rulers didn't wish to encourage separatism, the boundaries of the majority of provinces were set already during the Qing, Ming or Yuan dynasties.
Prefecture 地区 (dìqū) - The number of prefectures is changing often, currently there about 335 prefecture divisions in China. Throughout the years there are less and less 'prefectures' and more 'prefecture-level cities' (地级市 dìjíshì), which together with about 30 autonomous prefectures (自治州 zìzhìzhōu, designated for ethnic minorities) make up China's provinces.
County 县 (xiàn) - There are almost 3000 county-level divisions in China, among them about half are 'counties', while the other half is comprised mostly by districts (市辖区 shìxiáqū), former municipal regions which have become counties, county-level cities (县级市 xiànjíshì) and autonomous counties (自治县 zìzhìxiàn).
Township (乡 xiāng, 镇 zhèn) - Township in rural areas are usually called 乡, while in urban areas the township-level division is into 'towns' 镇.
Under the township-division an even more specific division into villages 村 (cūn) exists, but such bodies have no prominent political meaning.
Note that the term 市 (shì), normally translated to 'city' can in fact be a province-level municipality (such as 北京市), a prefecture-level city (such as 开封市) and a county-level city (for example 富阳 fùyáng in zhejiang province).
