Oddly enough, the best information that I could find on the topic seems to come from the DOT, in a 2003 FAQ (after the 2000 census) who suggest that neither one is 'suburbs' on their own, as they have some sort of an urban core to them:
What is an Urbanized Area (UZA)?
An Urbanized Area is a statistical geographic entity designated by the Census Bureau, consisting of a central core and adjacent densely settled territory that together contain at least 50,000 people, generally with an overall population density of at least 1,000 people per square mile. Within the transportation planning community Urbanized Areas are typically referred to as the UZAs. To learn more about Census geography, terms and criteria see http://www.census.gov/geo/www/
What is an Urban Cluster (UC)
An Urban Cluster is a new statistical geographic entity designated by the Census Bureau for the 2000 Census, consisting of a central core and adjacent densely settled territory that together contains between 2,500 and 49,999 people. Typically, the overall population density is at least 1,000 people per square mile. Urban Clusters are based on Census block and block group density and do not coincide with official municipal boundaries.
Unfortunately, their link to the Census terms & criteria is a dead link ... but the Census has a statement on one of their pages titled '2010 Census Urban and Rural Classification and Urban Area Criteria':
The Census Bureau’s urban-rural classification is fundamentally a delineation of geographical areas, identifying both individual urban areas and the rural areas of the nation. The Census Bureau’s urban areas represent densely developed territory, and encompass residential, commercial, and other non-residential urban land uses.
For the 2010 Census, an urban area will comprise a densely settled core of census tracts and/or census blocks that meet minimum population density requirements, along with adjacent territory containing non-residential urban land uses as well as territory with low population density included to link outlying densely settled territory with the densely settled core. To qualify as an urban area, the territory identified according to criteria must encompass at least 2,500 people, at least 1,500 of which reside outside institutional group quarters. The Census Bureau identifies two types of urban areas:
- Urbanized Areas (UAs) of 50,000 or more people;
- Urban Clusters (UCs) of at least 2,500 and less than 50,000 people.
“Rural” encompasses all population, housing, and territory not included within an urban area.
To summarize, the two 'urban' areas are both a town or city and its suburbs, but the delination between UZA and UC are if there are 50k people in that general region. I don't believe that you can use that designation to distinguish between urban & suburbs.