In terms of what it is, it is the complete elimination of all property. This distinguishes it from the more moderate Socialism in which only the means of production are collectivized. Under communism there is no property at all.
In the utopian versions they envision some sort of anarchy. As if. You'll need a very powerful state to eliminate property and keep it eliminated.
If that is the definition what of socialism, what would you call France and Demark, a hybrid?
My understanding of the popular meaning as used over here is a high degree of social programs and more control of business than we have here. Conservatives routinely call Europe collectively socialist as a pejorative.
Most economies are mixed economies, with varying degrees of various systems. I do not call European economies "socialist", because I know better, but then I'm not a conservative.
Even in the US we have a mixed economy, just like in Europe, but with varying degrees of the different systems.
Many cities have the utilities run by the city. Education is almost entirely run by the government. Those sectors are socialist - using the term without moral judgement.
Many states have highly regulated utilities, with very strict entry requirements and government granted geographic monopolies. Even the ability to raise rates is done by submitting a request to the government regulatory board. Those sectors are fascist - using the term without moral judgement.
It is clear that the monetary system in the USA is Monetarist - Fisher and Friedman.
The federal budget is very influenced by Keynes.
There is also a current of Welfarism, which idiots on both sides mistakenly call socialism.
There is also a current of Corporatism, where we have protections or subsidies for businesses.
Everything else in the economy, which can be most of the economy or can be tiny smidges of what is left over, is Capitalist. It is the state where you don't have government interference or control.
As an alternative to this analysis, which is useless and doesn't predict anything, I will provide the correct analysis.
Human societies need to sustain themselves by making things and consuming what they make. When the productive capacity entered a phase where a surplus could be made and hoarded, class divisions began to emerge in civilization. Classes are groups of people defined by their functional relationship to the means of production, i.e., to the elements that are required to sustain life and meet our wants and needs. The only distinction that matters is ultimately this one. State versus private, rich versus poor, and black versus white are all imperfect and unscientific categories for the purposes of understanding political economy. All that makes an actual difference is class: who hoards the surplus and who creates it, who monopolizes the implements of production and who rents their bodies out to the monopolizers, who establishes colonies in other people's land for resource extraction and who is colonized.
As class divisions emerge, due to the material advances in productive technology, there emerges an apparatus that functions to manage conflicts between the classes by the use of coercion. This is called a state. The phases of production in human societies were all accompanied by a state that made sure the dominant class retained its dominance, which sometimes meant providing concessions to the submissive classes to prevent their revolt. The same is true today: in capitalist societies, the state primarily serves the interest of capital. So, no Jason, publicly funded education is not socialism. In a capitalist society, the state funds educational institutions whose job it is to prepare workers for productively generating wealth for the owners of capital. This doesn't just cover public schools, obviously, but private schools with generous endowments and acres of tax free property, and state funding for research that takes place in both public and private universities. This is not socialism; this is the dominant class leveraging the state apparatus to extend its influence, while the lower classes struggle for concessions.
The question, then, is not whether the state or private sector is in charge of the economy, it's whether the owners of capital are the dominant class or the workers are the dominant class. Following a revolutionary overthrow of a capitalist or feudal-capitalist economy by the workers, there will exist an uneasy continuation of class struggle. This can last for decades, perhaps a century. During this period, which Marxist-Leninists refer to as socialism, the working class uses the state to limit and oppress the remaining capitalist class and defend the revolutionary movement from internal and external threats. All socialist experiments that have succeeded for longer than a few years have adopted this strategy, first defined by Lenin in
The State and Revolution.
Conversely, private enterprise is not necessarily antithetical to socialism. Remember, socialism is a transitional state, and depending on the conditions wherever the revolution has occurred (especially if it is emerging from a period of being dominated and suppressed by capitalist powers), the capitalist mode of production may be leveraged under the control of the workers' state to accelerate production and attract investment. In other words, to build wealth and gain power and influence in the capitalist world. To make capitalist societies depend on the workers' state instead of just trying to snuff it out. Sound familiar?
This is why all comments to the effect of "China is capitalist now" or "Venezuela became capitalist in the 2010's" are facile if they don't differentiate between adopting the methods of capitalism to build socialism or ceding the dominant class structure to capitalists. The USSR became capitalist. China is still socialist, which is again defined as a transitional stage that can (and perhaps must!) include capitalist elements. While China's heavy state regulation may resemble the social democratic reforms of Norway, they are not in the same phase of political economic development for this very reason. Norway is not building socialism, but managing capitalism in a way that placates the working class more than some other countries, in a way that makes sense for its particular conditions and resources. China is
building socialism in a way that makes sense for its particular conditions and resources, not abandoning it in favor of capitalist domination with welfare policies. As such, Norway is allied with the imperialist colonizers of the world, while China is allied with the anti-imperialist, colonized, impoverished nations.
The liberal reduction of these forces and their representative interests to "authoritarian" versus "democratic" is metaphysical, not materialist.