So this is a mostly American view of cities, and of course with American local government there are exceptions to every rule. For example most cities are a level below county government... but not Baltimore, which is independent from any county (including neighboring Baltimore county to the north) and is functionally a county level government. Cities generally have either a mayor and city council or just a city council (And how much executive authority the mayor has is dependent on the city charter... a city council could have all the executive powers and they mayor is merely a figurehead... or the system could be a city version of presidential government, sans judiciary (there is no judiciary lower than state government).
Generally a mayor will act as the executive and city council will act as a legislature (Any law they pass is called an "ordinance"). Mayor will usually name the police commissioner or chief or whatever the title is, though there might be a separate position for county Sheriff (in the 48 states that have them, Sheriff's are county level offices. In 46 states, they are also elected offices with career employees being "Deputies"). To give an example Los Angelous has both the LA Police (LAPD) and the LA Sheriff's Department (LASD). The former polices just the city of LA while the later polices all of LA County (which is the county the city is located in, but not all of LA county is the city... although urban sprawl might lead you to think otherwise. To whit, Compton is not part of LA City but it's own separate city... that is on the border of LA City).
As for working size that's harder as many modern cities are prone to commuting and a day time population can be a lot higher than a night time population. This is especially true in most cities not just American ones. Some Wards in Tokyo (Cities in their own right) are so prone to this that a day time population is three times the night time population. Shibuya Ward (home to the famous Scramble Cross Walk, which an estimate 3,000 pedestrians travers on each cycle) has only 200,000 residents living there. Most cities have commuter towns which are more open and less densely populated neighborhoods outside of the city limits that workers will visit. This makes jobs and actual residents difficult to ascertain (There are some people who have a residence in the city for working... and then fly home to their real residence for the weekend... especially true if you're living in a capital city).
It should be pointed out that most cities are built around the most important resource to all of them: Water. Cities generally aren't known for commodity harvesting (gathering resources) but rather commodity exchanging... Large cities usually got that way because they were major transportation hubs that local rural producers could sell their stuff to people who would use it to make things (Manufacturing) or sell it to others who would (Commodities Markets) or ship it to other places (Transportation and Logistics centers). There are some exceptions (L.A. is on an oilfield. There are oil pumps... some hidden in plain sight) but usually, water ways were one of the oldest transportation methods and most cities have a river or port near their oldest districts.
As such, most cities will source basic resources from other places where they are harvested (Generally, there are a few broad categories: Forestry Products, Agriculture Products, Mineral Products, Energy/Petro-chemical Products, and Fishing Products. Only the latter really can be produced by a city, if they have good access to fisheries). Manufacturing and Service Economies are more city's reason for being (Manufacturing is turning raw harvestable products into something else, Service Industry is selling of products as well as skills (such as computer coding or legal representation).
Other aspects would be architecture influence, cultural influence, sports preferences, whether the city is on the rise or decline (I like to ask which would you see it as: Metropolis or Gotham) nicknames or affectionate names, important buildings and landmarks, districts, and icons, favorite foods (New York is associated with Pizza and thinks all other Pizza is terrible. Baltimore and San Francisco are associated with seafood in general, crabs in particular (to the point that when their football teams faced off in the Superbowl, the Mayor of each city bet that the loser would deliver their local crabs dinner to the mayor of the winning city). Miami has Cuban food, Philadelphia has Cheesesteaks, New Orleans has Po' Boys and Cajun food in general, Seattle has coffee... ect.).
One film to look at with an eye for cultural differences is the original Parent Trap, where the twins, separated at a young age, decide to swap places and go live with the other parent on the other side of the country. While both parents are wealthy, down to earth, and moderately conservative by the 60s standards, the Father (Californian) has a more live and let live attitude and is more working class (he owns a vineyard... there's a lot of money in that, but he's at the end of the day a farmer) while the mother is a lot more concerned with the family legacy and keeping up appearances with Boston society (one example, from the moment we meet the Father, he makes it clear that his daughter is his number one priority, while the mother canceling her busy schedule to spend some one on one time with her daughter is a major point in her character arch). It should be pointed out that at the time the film was made, both settings were much more conservative leaning than the reputations they have today. California only voted for a democrat president once from 1952 to 1992.
While both had a lot in common in the big picture, they both have different attitudes over all based in part on the fact that they live in culturally different places, even in the same country.