I think the important thing to highlight here is that:
What are these things anyways?
Don't forget that Social Explorer makes it very easy to find geographies with an Address Search or by asking for multiple geographies. If you want to find information by an address, start with the Mapping feature. If you want to pull multiple geographies, start with the Table feature.
Each geography comes with a geographic identifier called a FIPS code. This code helps track geographies, which is useful when you need to join different Census tables or other non-Census surveys, or map Census data with a GIS.
FIPS codes for smaller geographic entities are usually unique within larger geographic entities. For example, state codes are unique within the nation, and county codes are unique within the state. Let's take a look at the first 3 county FIPS codes in Virginia:
The first two digits - 51 - represent the Virginia state FIPS code, and the last 3 digits represent the counties within Virginia.
In Virginia, all municipalities incorporated as cities are "independent cities." While almost all American cities are embedded within a single, or possibly multiple, counties, Virginia cities are not. For example, the City of Charlottesville exists as an independent city, with the donut of Albemarle County surrounding it. Charlottesville is not part of Albemarle.
The census handles Virginia independent cities BOTH as cities AND as though they were counties. You can find independent city data in county-level tables, which is convenient when you are pulling data for several Virginia counties.
The curious might enjoy this Wikipedia entry on the history of independent cities in Virginia:
If you are interested in the differences between urban and rural areas, do yourself a favor and read up on the Census's definition of those areas.
The Census Bureau identifies two types of urban areas:
“Rural” encompasses all population, housing, and territory not included within an urban area.
Just for fun, here is a link to the 2010 Census - Charlottesville Urbanized Area map. Notice that it is larger than the Charlottesville city limits.