Affordable Housing (formal sense), is specific housing units that are regulated to increase their affordability to certain population groups deemed to be disadvantaged. Typically those groups comprise households with income below some specified percentage of Area Mean Income (AMI) -- either income at time of application, or ongoing.
In the more general sense, "affordable housing" (uncapitalized) is any housing option which is deemed to be affordable to a given household or population. A widely-used standard definition of "affordable" offered by the US government's Housing & Urban Development agency is, housing costing no more than 30% of a household's gross annual income.
For a given area, "affordable housing" (uncapitalized) may be defined as that housing deemed affordable to a household of media income in that area.
"Most of the literature on affordable housing refers to a number of forms that exist along a continuum - from emergency shelters, to transitional housing, to non-market rental (also known as social or subsidized housing), to formal and informal rental, indigenous housing and ending with affordable home ownership." ("Affordable Housing" entry).
In some contexts such as Bay Area housing discussions, it is common for some parties to use "affordable housing" (uncapitalized) when tacitly or explicitly meaning the case of housing, typically new construction, where units are specifically rent, initial price, or equity-limited, i.e. Affordable Housing in the formal sense as above. However, since this is just one type of affordable housing approach, to avoid confusion, alternate terms such as "BMR" (Below-Market Rate), "non-market rate," or Inclusionary Housing may be used, or the term used capitalized ("Affordable Housing") to indicate the more formal sense intended.
Most commonly in San Francisco, Affordable Housing refers to rental housing units, although there are also programs to to make unit ownership more available to lower-income households.