Why is the Park Hill apartment complex (in S.I.) referred to as "the projects"?

I've always been curious about this...

It is not NYCHA housing. So how could it be "the projects"? No one calls Lefrak City (Corona, Queens), Vanderveer (Flatbush) or Diego Beekman (Bronx) "the projects"...

I am not arguing whether or not it's an impoverished/high-crime area, but just that it isn't the projects...

Thanks!