Not quite. Your conflating several things. Rent control is different from rent stabilization is yet different from rent increase laws. Often cities have all 3.

In SF the rent controlled properties, both for rent and for sale (yes you can buy super affordable apartments in SF if you don't exceed certain income) folks just have to make less than a certain amount a year. The income tiers are listed here, and are higher than I expect some would expect. https://sf.gov/reports/may-2022/income-and-rent-limits-inclu...

There is also a citywide rent increase cap of 3.6% currently (its calculated based off inflation and other factors) on any and all rental units, regardless of income or rent control status : https://sf.gov/information/learn-about-rent-increases#:~:tex....