Reference: http://homeguides.sfgate.com/hud-guidelines-low-income-1911.html
In addition, Section 8 housing, which has a movable housing voucher and the most options, uses the lower 50%-of-median threshold ("very low income"). The housing that has the higher 80%-of-median limit is in public housing, which has fairly recently gone to that higher limit partly to improve finances (if you have higher income, you pay more rent, though it's still subsidized), and partly to encourage mixed-income communities rather than filling "the projects" with 100% extremely poor people, which has in the past been blamed for turning them into high-crime ghettoes. Nonetheless they still have a poor reputation as places to live, and tend not to be very successful attracting middle-class residents, even with the subsidy.