No. Social housing is government owned and rented. Singapore is government built and sold. Singapore is a tiny island with little space. The government has to control what is built where and avoids it turning into Hong Kong slums.
>Public housing, also known as social housing, is subsidized or affordable housing provided in buildings that are usually owned and managed by local government, central government, nonprofit organizations or a combination thereof.
Wikipedia says 'usually'. And, yes, you are right that the individual HDB flats are typically owned by individual families (though the government also owns some and rents them out, but that's the exception).
However, HDB still does a lot of the managing. Eg HDB manages the lifts and other common spaces. They organise getting the exterior repainted, or general upgrading works to plumbing etc.
HDB also subsidises the price of a flat when you buy directly from them. There's a reason they have maximum income caps for buying.
My unpopular opinion: HDB should declare victory and go home. They more than solved the original acute housing shortage they were created for.
---
Singapore does a lot of things right. And HDB is, as usually a lot more competent than pretty much any other public housing programme anywhere else in the world. But that doesn't mean everything Singapore does (including HDB) is automatically a good idea forever.
Just like our local recreational drug policy could probably be improved by moving closer to what we do with the casinos. And the ban on vaping is just silly.
> However, HDB still does a lot of the managing. Eg HDB manages the lifts and other common spaces. They organise getting the exterior repainted, or general upgrading works to plumbing etc.
By that logic every apartment block is public housing.