I recommend backing up a bit so that we can frame these questions.

One of the more pointless questions anyone asks is a simple binary of, "is XYZ socialist?" Being real people doing real projects in the context of global capitalism and relentless imperial oppression, there is no such thing aa purely socialist, but many things are projects by socialists to advance socialism. When people learn this, they start to use the term as a shorthand: "my communist organization is socialist", "the Cuban revolution was socialist", "China is socialist". These claims only mean that the project is a socialist one. This is different from saying any of those projects have achieved socialism. None of them have and I have yet to meet a socialist who defends China while saying they have achieved socialism.

So really, this is a question of semantics and language using similar or identical terms with different meanings, and this is one of the reasons why those who read up on the topic have such a dramatically different opinion from those who do not.

So, for example, China has a stated ambition of becoming socialist within the next 30 years or so, setting concrete targets for what that means. And it is still a socialist project created and maintained by socialists.

Regarding owning the means of production, this is a Marxist concept. Marx's postulate was that the ruling class is that which owns/controls the means of production and that society is then crafted according to the interests of that ruling class. Under feudalism, the ruling class was landlords (own/control land), with the major underclass being peasants, serfs (they work the land). Under capitalism , the ruling class is the bourgeoisie, those who own factories, shops, etc and the major underclass is workers, those who work in the factories and shops. Marx hyoothesized that the proletarians who work in ever-concentrated companies would have the capacity to take the means of production by force and then continue running it themselves.

So why am I giving this crash course in Marxism? Well, because Marx himself described the period in which the working class had seized the means of production from the bourgeoisie not as socialism, but as the dictatorship of the proletariat. A period in which society still functions as capitalist in many ways, as the mode of production has not changed and production itself must be maintained, and the bourgeoisie still exist, but in which the working class has become dominant and can oppress the bourgeoisie. China is firmly in this category, exactly what Marx described as this transitional period of unstated duration, attempting to survive and thrive while under constant pressure from imperialists.