in ancient Chinese, we normally use single character for word. now we combine two single character with simliar meaning into one word. with that been said, 城 is like a castle/urban area, 市 is like market, 城市 is city

城 is the walls of an ancient city. its function is to keep people from the danger such as invasion or animal attack. Great wall is definitely a 城。 市 means a market where many people live together or gather together to trade each other or interact each other. Now I'm sure you've been clear with the meaning of 城市。 A huge market surrouded by walls. Modern city is built up without walls but we still use 城市 to express.

城 is a high walled enclosure to contain dwellings. For example, the Great Wall, 長城 for it encloses many dwellings. In modern Japanese it means a castle because of its high walls for protecting a small dwelling. 市 is a market. 城市 literally means "a market enclosed by high walls". Every old Chinese city is enclosed by high walls with four gates (entrances) and every city there must be a market. So in modern terms, it just mean a city with the "market" omitted.

城 we call the great wall is changcheng, however changcheng is long cheng (长-城） in Chinese.cheng could means old living buliding.Like 成都是一座古城 （chengdu is an old city) 市 could be mall or city. But we don't usually use '市‘ by itself. In Chinese, we don't usually distinguish 城 with 市，so 城 and 市 could both translating to city.Afterall,we don't use 城市/市 in ancient Chinese，we just called 城。 City belongs to province.To sum up,all these words are noun， 城市 is commonly used。