Subsidized housing is generally the name for a property where your rent is based on approximately 30% of your monthly income, and the Federal Government pays the difference (this is called subsidy). At these locations, your rent is always tied to your household income and you may be eligible for some medical or childcare expenses, which could lower your monthly rental amount. This subsidy either comes from HUD, or USDA-RD, depending on location.
This type of housing is NOT subsidized, however, the monthly rent is lower than the market rents for a given area. For example, these types of properties have rents that are usually several hundred dollars below market, and may range between $800 to $1300 depending on location and bedroom size. In order to live at one of these properties, your household income must be enough to afford the rent, yet not exceed certain income limits for the area.