What is the difference between a "town" and a "city" in the USA?

Here is a masterpiece of United States officialese gobbledygook:

https://www.census.gov/content/dam/Census/data/developers/understandingplace.pdf


But, if I am reading it right, the Census Bureau draws the line between towns and cities at a population of 50,000. If anyone comes up with something else from that verbose tangle, I’d welcome their interpretation.
In my little village, we have a town council but city limits, so I suspect the two terms are much more fluid.

The difference between a town and a city is a legal definition. The website below gives a *very* simplistic definition. The "Read More" option does mention that some states do have legal definitions of a town. I know New York State does because I live there.

Voters have to create and approve a city. State and county laws govern what a city can and can’t do. Towns, villages, communities or any other collection of people that are unincorporated have no legal standing by themselves. This means that county governments have to provide services to these groups instead, usually on an unofficial basis. There are exceptions since some states actually define what a town means legally and give this legal standing some powers.

https://www.reference.com/geography/difference-between-town-city-3fac131a417e7a77#

The difference between a town and a city in the United States varies state by state. An incorporated city is a legally defined government entity usually with its own elected officials, laws, and police force. A city may provide government services to its citizens. A town is unincorporated and is often smaller than a city. A town has very limited or no government powers with the county providing governmental services. A town may have a mayor and local ordinances which are very limited in scope. It is confusing. As an example, my county of 40,000 has two cities, one with 6,200 and one with 7,650 souls. My county also has 11 "towns". There are towns in California with 230,000 or more people. Also, more cities are reverting to town status as a cost saving measure.

https://www.thoughtco.com/difference-between-a-city-and-a-town-4069700

Because of the variation in law among states, even that definition is too specific to be entirely correct. For example, in California, there is no real difference between a city and a town; you can (and do) have incorporated "towns". In fact, that's true in some other states. Then there is my former home state of Ohio, municipal corporations can be either a "city" or a "village" depending on population, with a requirement of at least 5,000 people at a census to become a city; an unincorporated area is a "township", not a "town", and does depend on county services (at least in some areas). I used to live in a township in Ohio that had over 10,000 people, but that didn't make it a city -- because it wasn't incorporated (and there wasn't any push to incorporate, because half of the population of the township was included in the school district of a neighboring city that traditionally had good schools, and those people didn't want any change to the status quo).

http://codes.ohio.gov/orc/703

But, another exception: in New England, towns are incorporated (the town of Lexington, Massachusetts, for example, was incorporated in 1713) and generally provide all government services, counties are only ceremonial, and there is no size limit on a town; the real difference (at least in Massachusetts) is that cities are governed by mayor-council; while towns are governed by town meetings (which is why the town of Framingham, MA, with almost 70,000 people, narrowly voted this spring to give up its title of "the largest town in America" and become a city).

https://news.wgbh.org/2016/12/19/local-news/framingham-americas-largest-town-seeks-city-status

All this really shows is that the term "town" doesn't have anything resembling a clearly defined meaning, so the only way to really answer this question is to note that "city" does have a more-or-less-consistent meaning: an incorporated area that has a specifically-defined governing status under state law, and which may be separated from other incorporated areas by a population requirement (as in Ohio) or may require the consent of the electorate (as in Massachusetts). So to become a city, an area first MUST incorporate, and then it must meet whatever additional requirements are set out by its state for city status.