It might be interesting to do a breakdown of how nations are divided into subordinate units, in view of questions about town boundaries, smallest cities, and so on, that have shown up here over the past few months.
The United States is, of course, divided into fifty states, 13 of which came together in an indissoluble union to create the nation, and the other 37 of which have been admitted as equals by act of the Congress which they created. Each state (with one or two exceptions) is subdivided into counties, within which lie municipalities – and the terminology for these varies. The U.S. also has an autonomous “commonwealth,” a capital district (D.C.), and several small territories under its domain.
The United Kingdom was formed by the merger of the Kingdoms of England, Scotland, and Ireland, with most of Ireland breaking off as a separate nation in 1922. It too is broken down into counties with municipal governments.
Canada is comprised of ten provinces and three territories, with at least some provinces having counties and municipal governments.
Australia is likewise made up of six states and two territories, with a few outlying islands having territorial relationship to it. I don’t know the composition of Australia’s sub-state government structure.
In New York, the entire state is broken into 62 counties, five of which are parts of the City of New York. Counties have elected local governments, and are broken down into towns (akin to townships in the Midwest) which have local governments. Cities lie within counties but are not included within towns; villages are legally constituted municipalities within towns. Cities, towns, and villages all have elected local governments.
In North Carolina, counties have local governments, and have cities and towns lying within them with elected local governments. “Towns” in N.C. parlance are equivalent to villages in New York. Townships do exist in North Carolina, as a consequence of Reconstruction, but they are merely lines on the map subdividing counties, for convenience in assessing, land title, census taking, reapportionment, etc., and have no separate legal existence.
Cities in Virginia, along with about six cities elsewhere, do not lie within counties in a legal sense, but are separate local governments. AFAIK the other cities which are not within counties include Carson City NV, St. Louis MO, and Baltimore MD. (And there are St. Louis and Baltimore Counties which include suburbs of those cities but not the cities themselves.) In some cases, city and county are coterminous, and often have a unified government exercising both city and county functions; these include Indianapolis IN, Nashville TN, and San Francisco CA.