Urban area
An urban area is a human settlement with high population density and corresponding infrastructure. Urban areas are created through urbanization and are categorized by urban morphology as cities, towns, conurbations (the merging of several towns), or suburbs.
In contrast, rural areas refer to areas with low population density, such as villages and hamlets.
Historically, urban revolution led to the creation of civilizations with modern urban planning that — along with other human activities, such as exploitation of natural resources — leads to human impact on the environment.

Urban areas are created and further developed by the process of urbanization. Urban areas are measured by various means, including analyzing population density and urban sprawl.
Unlike an urban area, a metropolitan area includes not only the urban area, but also satellite cities plus intervening rural land that is socio-economically connected to the urban core city, typically by employment ties through commuting, with the urban core city being the primary labor market.

Rural area
In general, a rural area or countryside is a geographic area that is located outside towns and cities. The word "rural" encompasses "...all population, housing, and territory not included within an urban area. Whatever is not urban is considered rural."
Typical rural areas have a low population density and small settlements. Agricultural areas are commonly rural, as are others, such as forests.

Different countries have varying definitions of "urban" and "rural" for statistical and administrative purposes.

The United States
- An urbanized area consists of a central city with surrounding areas whose population ("urban nucleus") is greater than 50,000. The area may or may not contain individual cities with 50,000 or more; rather, it must have a core with a population density generally exceeding 1,000 persons per square mile; and may contain adjoining territory with at least 500 persons per square mile- .
- A rural area comprises open country and settlements with fewer than 2,500 residents; an area designated as rural can have a population density as high as 999 per square mile or as low as one person per square mile.
Canada
The term "population centre" has replaced the term "urban area." Both terms are defined by population count and density.
A population centre is an area with a population of at least 1,000 and a density of 400 or more people per square kilometer. A rural area is where the population is fewer than 1,000 inhabitants and population density is below 400 people per square kilometer.

Adapted from Wikipedia, the free encyclopedia. Internet. Accessed on June 14, 2016.
Adapted from Statistics Canada. From urban areas to population centres. Internet. Accessed on September 17, 2019.