城市chéng shì :人口密集、工商业发达的地方,通常是周围地区政治、经济、文化的中心. 都市dū shì ：国家的主要城市；大的城市. 都会dū huì 表示都市的意思。都，原意是建有宗庙的城邑，后来引申为城市；会，人物荟萃的地方，主要指城市。 都会的城市意思至迟在西汉出现，唐孙逖：“会稽郡，海之西镇，国之东门，都会蕃育，膏肆兼倍“。宋朝孙因《越问·封疆》：绍兴古今之大都会，为九牧之冠冕。 大都会：大都市，出自《宝庆会稽续志》绍兴襟海带江，方制千里，实东南一大都会。

都市 and 城市 are the same thing that mean 'city', they are just synonym. When I think of 都会 this word, it will be coming off a picture of city of night in my mind.

都市 in my opinion is closer to "main city". 城市 just means "city". 都会... no idea. I tend to see this as part of a name, rather than refer to "a large built-up area". Urban meeting place perhaps? Some of the meanings get a bit muddied over time. Like Myeongdong, Insadong, etc. in Seoul. Why are there so many holes in a city?