Here are some varieties of "socialism:" command socialism, market socialism, socialist market economy, social democracy, democratic socialism, right wing socialism, utopian socialism, corporate socialism, just plain vanilla socialism. Here are some people who have claimed to be socialist, some of them selecting one or another of these types, but some just keeping it plain vanilla generic: Kim Jong-Un, Xi Jinping, Stefan Lofven, Nicolas Maduro, Bernie Sanders, Aexandria Ocasio-Cortez (AOC). Who is really a socialist and can we make any sense of all this?
Among the strictly economic issues involved here, aside from the political ones, there are three that stick out prominently: ownership, allocation, and distribution. The first may be the most important, or at least the most fundamentally traditionally classical: who owns the means of production? This is bottom line Marx and Engels, and they were unequivocal: socialism is state ownership of the means of production, even though in the "hiigher stage of socialism" generally labeled "pure communism," the statte is supposed to "wither away." Capitalism is private ownership of the means of production, although there are debates over some intermediate collective forms such as worker-owned collectives, something favored by anarchistic and utopian socialism and its offshoots and relatives.
Regarding allocation the issue is command versus market, wiith command in its socialist form coming from the state, although clearly a monopoly capitalist system may involve command coming from the large corporations, with this reaching an extreme form in coeporatism and classical fascism, sometimes called corporate socialism. Needless to say, it is possible to have state ownership of the means of production, classical socialism, but some degree of markets dominating allocative decisions.
Then we have distribution. In the Critique of the Gotha Program, Marx said the goal of communism was "from each acording to his ability, to each according to his need." Emphasizing if not precisely that at least a focus on minimizing poverty and supporting those in need as well as increasing the overall level of income and wealth equality is another element of many forms of socialism. This focus has been especially strongly emphasized by social democracy and its relatives, although most forms of socialism have at least officially supported this, if not always in practice.
Regarding our list of socialisms, where do they stand on these three, adding in the big political issue of democracy and free rights versus dictatorship, well: command socialism involves as its name suggests both command in terms of allocation combined with state ownership of the means of production, with no clear outcome on distributional view. Historically permanent command as a system has coincided fully with dictatorship, including when this occurs with capitalism as in fascism, especiallly in its German Nazi form, a nearly pure form of command capitalism. The classic model of this form was the USSR under Stalin, with its leading current example being the Democratic Peoples' Republic of Korea (DPRK), aka North Korea, which pretty much tells us what kind of socialist Kim Jong-Un is.
Market socialism combines state (or collective) ownership of the means of production with market forces driving allocation decisions. The old example of this that also had that holdover from utopian socialism of workers' management, was Tito's not-so democratic Yugoslavia, which blew up, although its former provincce of Slovenia eventually was the highest real per capit income of all the former officially socialist nations. According to Janos Kornai, market socialism, including his home of Hungary, suffered from the problem of the soft budget constraint, although we have seen that in many mostly market capitalist economies with rent seeking powerful corporations.
There is no clear difference between market socislism and the "socialist market economy," but the Peoples' Republic of China (PRC) has gone out of its way to officially label itself this latter term, perhaps due to the collapse of Yugoslavia. Many, including the late Ronald Coase, claim China is really capitalist, but in fact while there is now much private ownership, state ownership remains very strong, and while there is no longer organized cental planning, command elements remain important, and the ownership situation is very complicated, with many firms having substantial while partial state ownership. In principle this form could be democtatic, but it is not at all that in Xi's current PRC, which has had a largely successful economic system for the last four decades, despite high inequality and other problems. In any case, this is the system Xi Jinping is identified with.
Social democracy now is the form that emphasizes distributional equality and support for the poor over the ownership and alllocation elements. This is now, most dramatically in the Nordic nations, although it has had a weaker version in Germany in the form of the social market economy. The name "social democracy" comes from the now century and a half old German Social Democratic Party, within which at the end of the 19th century several of these forms debated with each other, although in the end what came out, inspired by the original "revisionist" Eduard Bernstein, was what we now call social democracy, which is indeed politically democratic and supporting an expansive welfare state, while not pushing either state ownership or command. Stefan Lofven is the current prime minister of Sweden and also leader of the Social Democratic Party of Sweden. A welder and union leader, Lofven just managed to get reelected and form another government last month, although his new government is "moving to the center," and while he is certainly a social democrat, he has also described himself as being a "right wing socialist," and Sweden has pulled back somewhat from its strongly social democratic model over the last quarter of a century.
Which brings us to democratic socialism, currently highly faddish in the US given that both Bernie Sanders and AOC have identified themselves as followers of this ideology. The problem is that of all the others mentioned, this one is the least well defined, and Bernie and AOC themselves seem to disagree. Thus when pushed Bernie posed Denmark as his model, which is a leading example of social democracy, arguably more so even than Sweden now, although its current prime minister is not a Social Democrat (party) and argues that Denmark is "not socialist" (noting its lack of command state ownership). But AOC has at times said that democratic socialism is not social democracy, while exactly what it is remaiins not well defined.
One source might be the platform of the Democratic Socialists of America (DSA), which AOC officially belongs to. This supports a democratic and decentralized form that emphasizes worker control, if not clearly ownership, with this harking to utopian socialism, with an ultimate goal of state or some other form of collective ownership, but not in this document command. AOC herself has now pushed forward the Green New Deal, (GND) which should perhaps be labeled "Green Socialism," yet another form. I do not wish to get into a discusson in this post of the details of the GND, regarding which there has been some confusion (retracted FAQ versus 14 page Resolution) about which there remain some uncertainties. DSA has at times nodded to the British Labour Party, which after 1945 under Clement Atlee, both nationalized many industries while expanding the social safety net, while avoiding command central planning. However, the GND seems to avoid nationalizations, while emphasizing a major expansion of rhe social safety net, along with some fairly strong command elements laregely tied to its Green environmental part, arguing that mere market forces will be insufficient to move the US economy off its current fossil fuel base soon enough.
Which brings us to generic socialism and the still not described Nicolas Maduro, President of Venezuela. He is loudly describing himself a socialist, but what form, if any, is unclear. But his economy is the biggest current economic disaster on the planet, so his ongoing claims of being a socialist are damaging the label, as seen in the eagerness of conservatives to identify socialism with him and denounce people like Bernie and AOC and all the Dem prez candidates signing onto the GND even before they knew what was in it, with this exemplified by Trump ranting loudly on this theme during his SOTU.
Looking closely it seems that indeed Maduro and Chavez before him, who preferred labeling the system "Bolivarianismo" rathet than "socialism," did carry out portions of various of the forms of socialism. Many firms were narionalized, with currently the number of privately owned firms about half of what there were 20 years ago (when Chavez was elected), although many of those original firms have simply disappeared. About 20% of farmland was nationalized, mostly large-scale latifundia, supposedly to be turned over to landless peasants. But much of it has simply come to be uncultivated by anybody. In any case, there remain large portions of the economy privately owned, with still wealthy owners living in gated communities and not suffering.
Perhaps the most damaging of the socialist policies have been scattered efforts at command, not based on any central plan, especially using price control. In agriculture this has been a complete disaster, especially once hyperinflation hit. Food production has collapsed, and lack of food has driven 3 million out of the country, with many still behind having lost much weight. OTOH, the regime is supposedly being green by emphasizing traditonal local crops. But this is not even a joke. Bolivarianismo's main positive was its popular redistribution policy, which increased real incomes in poor areas, especially while Chavez was in power, borrowing from the social democracy model.
The problem here is that all of these things, even many oof them together, have been recently tried in neighboring nations, such as Bolivia, without simialrly disastrous results. Somehow Venezuela has just completely blown apart, with reportedly 86% of the population now opposed to Maduro and people in the poor neighborhoods of Caracas who were the Chavismo base now out demonstrating in large numbers (and being violently suppressed) after Maduro got reelected in a clearly fraudulent election, with most of his neighbors calling for his removal.
I think two things not related specifically to socialism have played crucial roles here: corruption and hyperinflation. The most important agent in the Venezuelan economy is the state-owned oil company, which was nationalized long before Chavez came to power. But he, with Maduro made this worse later, fiirng the competent technocratic managers of that company and replacing them with political cronies, with the outcome being a serious decline in oil production, this in the nation with the world's largest oil reserves. Which leads to the other problem, massive corruption, with the incompetent cronies at the top of the state-owned oil company the worst. The other killer item has been the hyperinflation, whose source I do not really know, although Venezuelan tax rates are lower than those in the US. Certainly part of it is massive budget deficits, and as the MMT people note, they were borrowing from abroad. I do not fully understand all involved in the hyperinflation, although that is not a standard phenomenon in a full-blown command socialist economy, but the hyperinflation has clearly been the final killer of the economy, collapsing support for Maduro. Apparently about a third of the population still supports "socialism," while many of those people reject Maduro, claiming he has blown what Chavez implemented, which Maduro certainly has.
So, for a summary. Command socialims a la the DPRK is an awful diasster, famine plus dictatorshiip. Market socialism/socialist market economy a la China has been good at rapid economic growth and much else, although suffering many ills on the environment and income distribution, not to mention alo being dictatorial. Social democracy a la Swden and Denmark has done as well as any economic system on the planet and is democractic and free, but has also suffered from various problems. The "democratic socialsim" of certain American politicians remains poorly defined and is in danger of being tied to the disastrous and vaguer form of "socialism" happening in Venezuela, with the danger for US politics being that conservatives may actually succeed in tying this pooerly defined democratic socialism with the barely socialist disaster in Venezuela.
Personally, I wish that Maduro would stop calling himself a socialist. Then he should also resign and get lost for the good of his people ASAP, although I do not support overdone US efforts by sanctions or possible invasion to bring this about. Let it be the Venezuelan people who remove him, however.