Yes. Rent control is what most people are familiar with (grandma living in a beautiful 3 bedroom apartment in Greenwich Village paying $200 / month, locked in since the 1970's). Rent stabilization is just a regulation that puts some type of reasonable cap on how much landlords can increase the rent every year, usually around 3-5% per year.

This is especially relevant in this election, as Cuomo is attacking Mamdani for living in a rent stabilized apartment, suggesting it's hypocritical because he can afford a more expensive apartment. This is deliberately trying to muddy the distinction between "rent stabilized" and "rent controlled" (about half of NY apartments are rent stabilized, and there is absolutely no cultural expectation that people move out when they get a raise, or whatever nonsense Cuomo's suggesting).

I'm still not sure what the important distinction is. Are you saying it's that rent control freezes the price entirely, while rent stabilization allows it to increase? That doesn't seem to be right from what I'm seeing; "rent control" includes systems where the rent can increase. NYC apparently has both and NYC rent control does allow for (capped) rent increases, according to the NYC government: https://hcr.ny.gov/system/files/documents/2024/01/fact-sheet...

While rent controlled apartments can increase the rent, it's extremely limited, usually based on the landlord's expenses and not market conditions.

Rent stabilization is roughly based on the inflation rate, so, while tenants who've lived in one place for a while might be getting something approximately considered a "sweet deal", it's not the ridiculous scenario rent control can produce. One other relevant distinction, rent controlled units can be passed down to family, keeping the same rent rate. Rent stabilized apartments can also be passed down, but it's the same as if a new tenant was taking over—the price can be reset back to market rate.