"Singapore has one of the highest home ownership rate in the world, due to the commitment of our founding fathers since the very beginning of nation building. Today, there are more than 1 million HDB flats across the island, home to close to 80% of Singapore's resident population. The schemes highlighted below help Singaporeans meet their housing needs at different life stages."
So the dictionary says that HBD housing is public housing, wikipedia says that HBD housing is public housing, and the Singaporean government says that HBD housing is public housing.