Among many who have not engaged with Marxist theory, there can be confusion regarding the determination of systems as Socialist, Capitalist, and so forth. Are markets Capitalism? Is public ownership Socialism? Is a worker cooperative in a Capitalist country a fragment of Socialism? These questions are answered by studying Dialectical and Historical Materialism, and I will attempt to help clarify those questions here.
The idea that Socialism means only and exclusively full ownership in public hands is wrong, and anti-Marxist. To take such a stance means either Capitalism and Feudalism have never existed either, the sort of “one-drop” rule, or that Socialism itself is a unique Mode of Production that needs to be judged based on “purity” while the rest do not, a conception that has roots in idealism rather than Materialism.
Modes of Production should be defined in a manner that is consistent. If we hold this definition for Socialism, then either it means a portion of the economy can be Socialist, ie USPS, or a worker cooperative, or it means an economy is only Socialist if all property has been collectivized. Neither actually allows us to usefully analyze the trajectory of a country and who actually has the power within it.
For the former, this definition fails to take into account the context to which portions of the economy play in the broader scope, and therefore which class holds the power in society. A worker cooperative in the US, ultimately, must deal with Capitalist elements of the economy. Whether it be from the raw materials they use being from non-cooperatives, to the distributors they deal with, to the banks where they gain the seed Capital, they exist as a cog in a broader system dominated by Capitalists in the US. Same with USPS, which exists in a country where heavy industry and resources are privatized, it serves as a way to subsidize transport for Capitalists. The overall power in a system must be judged.
For the latter, this “one drop” rule, if equally applied, means Feudalism and Capitalism have never existed either. There is no reason Socialism should be judged any differently from Capitalism or Feudalism. To do so is to add confusion, and the origin of such a desire is from idealists who believe Socialism to be a grand, almost mystical achievement of perfection. The truth is more mundane, and yet because it's more mundane, it's real, and achievable, as it already has been in many countries.
What Socialism ultimately is is a system where the Working Class is in control, and public ownership is the principle aspect of society. If a rubber ball factory is privately owned but the rubber factory is public, the public sector holds more power over the economy. In the Nordics, heavy industry is privatized for the most part, and social safety nets are funded through loans and ownership of industry in the Global South, similar to being a landlord in country form. In the PRC, heavy industry and large industry is squarely in the hands of the public, which is why Capitalists are subservient to the State, rather than the other way around.
As for the purpose of Socialism, it is improving the lives of the working class in material and measurable ways. Public ownership is a tool, one especially effective at higher degrees of development. Markets and private ownership are a tool, one that can be utilized more effectively at lower stages in development. Like fire, private ownership presents real danger in giving Capitalists more power, but also like fire this does not mean we cannot harness it and should avoid it entirely, provided the proper precautions are taken.
Moreover, markets are destined to centralize. Markets erase their own foundations. The reason public ownership is a goal for Marxists is because of this centralizing factor, as industry gets more complex public ownership increasingly becomes more efficient and effective. Just because you can publicly own something doesn’t mean the act of ownership improves metrics like life expectancy and literacy, public ownership isn’t some holy experience that gives workers magic powers. Public ownership and Private ownership are tools that play a role in society, and we believe Public Ownership is undeniably the way to go at higher phases in development because it becomes necessary, not because it has mystical properties.
Ultimately, it boils down to mindsets of dogmatism or pragmatism. Concepts like “true Socialism” treat Marx as a religious prophet, while going against Marx’s analysis! This is why studying Historical and Dialectical Materialism is important, as it explains the why of Marxism and Socialism in a manner that can be used for real development of the Working Class and real liberation.
Marxism isn't useful because Marx was prophetic, but because he synthesized the ideas built up by his predecessors and armed the working class with valuable tools for understanding their enemy and the methods with which to overcome said enemy.
By the time we reach Communism, that is, the Marxist vision of a fully publicly owned and planned world economy, distribution of wealth will likely be based on need. There is no necessity for equal wealth, as humans have very unequal needs. Equal ownership of property is certified through public ownership.
If you're asking what's preventing someone from starting a business, it would be the sheer difficulties of actually starting one that can compete with the highly developed productive forces in the rest of the economy. Communism isn't so much about outlawing private property, as developing beyond it.