It can depend on the particular U.S. State. It's sometimes useful for non-Americans to think of the U.S. like a federation of weak semi-autonomous countries. Each state more or less runs their own affairs unless there's some federal interest in which case the national interest overrides the state one. What this means for this topic is that states organize their territories in sometimes different ways that can seem sometimes bizarre to outsiders.
For example, Connecticut divides itself into eight large counties and those counties are further divided into towns. Thus the meaning of "town" in Connecticut means a geographic subdivision and may have nothing or little to do with there actually being a cluster of buildings or even any interesting population at all. In fact, in Connecticut, a city is located within a town and is subordinate to it! Towns may set their own general method of local governance but are subordinate to their counties and then to their state.
Louisiana is divided into Parishes that mapped to the Catholic Parishes present in the 19th century instead of counties and are generally run by a governmental body called a Police-Jury which is a combined legislative/executive body with enormous local powers.
Virginia is divided into counties, which may have towns and other kinds of human settlements. But cities are independent of their surrounding county and act at a parallel level to counties in terms of political power. The county seat where the county government resides may or may not be in a city, but if it is there will be a parallel and equally powerful city government in the same area. Cities in Virginia, as defined governmental territories have very controlled borders, but may have very small populations. But in other areas, the cities are so large they no longer exist within a county at all and the historic county no longer exists. This has impacts mostly for taxes, schooling and property. But practically the most you would notice is that you could eat at a restaurant on one side of a street and cross to the other to get some coffee and pay a different sales tax on either side.
It goes on from there. From a practical standpoint, it almost entirely affects the locals and can be a deciding factor with where people choose to live. For outsiders, it doesn't matter much except that your sales tax might be highly variable as you transit through local governing zones.