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).

Socialism inevitably means state ownership only because states make themselves inevitable, not because state ownership is an inherent property of socialism per se. Plenty of examples exist of socialism working at a smaller scale, such as with worker owned cooperatives. If you're a programmer, you might own your own means of production. Free software is socialist in principle - all of that code is collectively owned.

But when the monopoly on violence gets involved, socialism often gets co-opted to serve the interests of the state rather than the people. I would argue that authoritarianism and and the creation of an elite centralizing and controlling wealth and resources for itself is as much a fail state for capitalism as it is for socialism, that it's just a different bunch of pigs feeding at the trough.

And to refer to your earlier comment, socialized provision of services is absolutely a form of socialism. If those services aren't being run for a profit under market principles, made available only to consumers who can afford it, and that profit isn't being captured to increase the wealth of private ownership, then it's a form of socialism.

In the US we have Social Security, Medicare and Medicaid, which are ostensibly socialist programs (certainly they were denounced as such when created.) One might argue that they aren't truly socialist since they don't collectivize the means of production but they certainly aren't capitalist in principle.

Of course it also helps to remember that "socialism" encompasses a wide spectrum of ideology and theory, and that if you get five socialists in a room and ask for a definition of socialism you'll wind up with seven manifestos and a fistfight. There are socialists who will argue for Soviet and Chinese style central control, and will point out (as capitalists will about capitalism) that socialism brought those states out of grinding poverty and vastly improved their peoples' quality of life, and others who abhor the violence and oppression of authoritarian socialism, believing it can only be achieved through nonviolence and voluntarism.

Point being that absolutist phrases like "socialism inevitably means state ownership" don't work as a useful critique because they don't consider the flexibility and adaptability of socialism as a concept. They tend to be thought-terminating cliches, like "capitalism is the worst system, except for all others," which serve to to normalize the premise that criticism of capitalism is futile because no useful alternatives to capitalism can possibly exist.