What is Public Housing?

Legal Definition
Public housing may be a form of housing tenure in which the property is owned by a government authority, which may be central or local. Social housing is an umbrella term referring to rental housing which may be owned and managed by the state, by non-profit organizations, or by a combination of the two, usually with the aim of providing affordable housing. Social housing can also be seen as a potential remedy to housing inequality. Some social housing organizations construct for purchase, particularly in Spain and to an extent elsewhere.
-- Wikipedia
Legal Definition
Public housing may be a form of housing tenure in which the property is owned by a government authority, which may be central or local. Social housing is an umbrella term referring to rental housing which may be owned and managed by the state, by non-profit organizations, or by a combination of the two, usually with the aim of providing affordable housing. Social housing can also be seen as a potential remedy to housing inequality. Some social housing organizations construct for purchase, particularly in Spain and to an extent elsewhere.

Although the common goal of public housing is to provide affordable housing, the details, terminology, definitions of poverty and other criteria for allocation vary within different contexts.
-- Wikipedia