You didn't do what I asked and thus you convinced me you don't know (posting a meme doesn't count). I'll be brief here:
Market Rate - a developer has a site, raises money based on expected demand, hires engineers and architects to design for it, hires construction company to build it, leases up and either holds onto it or sells it,
Affordable Housing - same as above but some of the money comes from the sale of tax credits or direct investment from the government. There are strings attached, typically either age-restricted or income restricted where residents have to make a certain percentage less than a average county income but enough to pay the rent. Frankly, it's a genius program for a lot of reasons I can point out to anyone interested,
Public Housing -- AFAIK we don't build this anymore but there are still lots of them around (it's been replaced by the success of Affordable Housing). Don't confuse this with Section 8, which relates to rent funding for qualified individuals for existing housing. It doesn't build anything new.
As stated earlier Rent Control goes back a long way. It helps people stay in their homes when a new landlord buys their building and would love to kick them out and make a huge profit. What kind of asshole would do this? You guessed it:
Now I'll ask you an easy question: have you been to NYC lately?