Depending on the state there may be different formal definitions based on population and incorporation status. In Ohio, we have townships, villages, and cities. In Pennsylvania they have “boroughs” instead of villages. In NY a borough is a subdivision of a city. I don’t think they have the township organizational structure in Vermont. In Maine there are unincorporated territories (usually just numbered).

The role of the county government can vary significantly from state to state too.

Most towns are not urban by any standard. I ate dinner over the weekend in a town with a population of 669. It was big enough to have its own restaurant and post office. It was a 30-40 minute drive from any town with a population over 10,000 (and that, just barely).

This guy has a YouTube channel of him just driving around small towns in the rural Midwest USA. https://youtube.com/@joeandnicsroadtrip