Towns and suburbs are generally classed as urban. Maybe low density urban, but urban nonetheless.

It probably makes sense. Having yards and trees and driving 2 miles to Target is more similar to not having trees and driving 2 miles to Target than it is similar to driving 200 miles to Target.

Have sidewalks? Probably urban.

A better dividing line is:

Given the choice, how would someone living there most often visit a grocery store?

In an urban area walking might be the common mode.

In a suburban area driving is OFTEN going to be the preferred mode, and even in small cities (particularly ones still small enough to have free parking at a nearby grocery store) driving there is still going to be preferred; at least in the US. In my experience Bellevue WA is a small, still suburban like city, while Seattle has crossed the anti-car (and expensive real-estate) line to 'big city'; but is neither old enough (pre-industrial grocery store layouts) nor big enough to be a healthy big urban city.

Offhand, I would define rural as any area where a drive to the third closest typical grocery store is at least a one hour round trip (by car, at legal speeds, including delays at any traffic device or from commute volume).

I wasn't trying to invent a dividing line, more trying to highlight how usage/understanding can vary. Here's some discussion from government statisticians:

https://www.ers.usda.gov/topics/rural-economy-population/rur...

Large swaths of the US are what that page calls 'micropolitan', centered around small urban clusters, which are the areas I think cause the most confusion, built up areas that are treated as urban in statistics and conversely thought about as rural by lay audiences.

Eh? In what most of the world would call a city, you don’t have to drive 2 miles to get to a store. You don’t even have to own a car.

There’s a reason that suburban is distinct from urban.

Urban doesn't mean 'metropolitan city', it means 'built up area'.