There are some common misconceptions of socialism here. However, here's a usual copy/paste that will clear any misunderstandings before any arguments start.
Sometimes when talking about economics, we talk about distribution and ownership. Ownership can range from cooperative or social ownership (socialism) , government ownership (state capitalism) , or capitalist ownership (capitalism). Distribution is usually how the goods and services produced by these systems can be distributed in society. Some ways of doing this is either through a planned economy or a market economy.
Capitalism and Socialism are systems of ownership. Capitalism is a system of ownership where property is privately owned. The goods produced on that property do not belong to the workers, but the one who owns the property. In turn, the owner may pay the workers a wage for using that property while the owner can do anything they want with the goods produced. Wealth is efficiently produced, but there's an issue as to where that wealth goes. Most countries in the world today are capitalist economies. Socialists reject this because it's an inherently hierarchical system of ownership.
Socialism advocates for a system of ownership where workers cooperatives own property. Workers democratically decide how the work place is run and how the business is done. This goes against the hierarchical structure of private property in Capitalism and State Capitalism. You can include markets in both systems since markets are an economic system of distribution, NOT a system of ownership. Pay is NOT the same for all workers, and is based on a democratically (or legally) agreed upon standard. Workers cooperatives do exist in modern society and are a growing alternative to capitalism because it ensures worker happiness and fair pay over fast paced wasteful efficiency. The idea behind Marxism is that socialists should take control either through elections or revolutions to set up a transition state where essential industries were centralized. This transition state would move on towards socialism. Government ownership is NOT socialism, this is a very common misconception and I'll explain briefly why people believe this.
There were two types of socialists before WW1; revolutionary and evolutionary socialists. Both were influenced by Marxism as the unifying principle for socialism, and so they believed only the state can bring about change. Revolutionaries wanted to overthrow the state through a revolution, and Lenin was the only one who was successful at it at the time. Evolutionary socialists set up political parties called democratic socialist parties and believed winning elections can bring about change. By the end of the day, Lenin was the only one that succeeded and so others followed to start up revolutionary socialist parties called communist parties. With the devastating effects of WW1, the Soviets decided to delay the transition to socialism by centralizing even more industry. Lenin called this, "state-capitalism." State Capitalism is a term used by Lenin to describe the fact that workers transition from going to jobs under an owner who owned a company, to the government that owned the company. By the time Stalin took over and Lenin was dead, Stalin moved on with government ownership of nearly all industry, and infamously declared, "this is socialism." People have been describing socialism as government owned industry eversince, even going as far as to call the Military as a socialist institution.
With the rise of the Internet, more and more people are starting to realize what socialism is. The Websters Dictionary definition is infamous for furthering the common misconception. Here are some other key facts about socialism:
For a look into how socialist companies can work, look into Mondragon corporation which is the largest worker owned cooperative and one of the largest, most successful companies in Europe. Compared to privately owned businesses, cooperatives provide a fairer share of income, and typically the decisions are made by the people who run them.
Socialism is generally seen as democratic socialism, which can include non-market socialists and market socialists. Non-Market socialists advocate for decentralized, local planning where the community makes the decisions on what to produce and what to support. This can include the concepts of industrial democracy or economic democracy. These concepts may also include consumer cooperatives (consumer planning).
Personal property is not the same as private property. Personally property includes your body, your house/car/phone. Private property is used to produce wealth and can include absentee ownership, for example: I live in Nevada and own most of the wealth produced by workers despite the property and workers being in New York. Things you produce yourself and sell are your personal property, and you can do whatever you want with it.
You shouldn't take people seriously when they say a society is a mix of Socialism or Capitalism (or advocate for such a thing), as that doesn't make any sense. What people mean by this is either Market Socialism, or a regulated capitalist economy.
Socialized welfare provided to the citizens of a society would have to be involved in a highly democratic society to be considered socialized rather than nationalized (state-ownership). Socialization would mean every citizen has a fair input and share of the product that is provided to them, it is where all of society owns and controls the distribution of a good/service and only answers to the public, not the will of rulers or a state. Socialization is organized democratically and is more transparent/responsive to citizen input. Nationalization focuses on elected government representatives to take on a role and elect other leaders to organize industry. Politicians and lobbyists own the means of production under nationalization. Nationalized industry switches the ownership of a private owner to the government. Many social democratic parties and democratic socialist parties have tried to make nationalized industry more democratic as a process while others have advocated restructuring them so that they are democratic. Look into economic democracy or industrial democracy for more examples of how socialization can work. While nationalization has been done by those who control the government for military purposes, saving an industry, or creating a monopoly.
Most socialist visions have advocated for some form of more representative democracies or council democracies. Council democracies are designed where everyone from the smallest unit of a neighborhood only vote and talk about issues in politics that affect them. Direct representatives are sent to higher councils where they represent larger issues on the city or state level. These types of systems are inspired by the Swiss and are currently in practice in Rojova. The soviets implemented council democracies in the form of a Soviet Democracy for an extremely brief time, but abandoned it. These forms of democracy make citizen input more direct and social without resulting in tyranny of the majority that other forms of democracy try to limit.
Societies considered socialist/communist or at least adhere to Marxist philosophy include Revolutionary Catalonia, Rojova (2016), and the Paris Commune. The USSR and China (among others) are not examples of socialism or communism since all they went through was the transition state and never even achieved socialism.
Despite the Marxist influence of nationalizing essential industry, these are not features of a socialist economy. A good reason for government control of an industry, according to Marx is to take care of the working class while transitioning to socialism. You will see socialists and social democrats support this since the NHS does have Marxist influence.
Marx described in his manifesto the short term solution of nationalizing transportation, communication, and most essential industries as transition from capitalism to socialism. This does not mean a communist society will include these things as it is stateless. Marx is influential in the sense that his ideas of socializing certain industries for the sake of the working class led to the social democratic parties developing the famous welfare states.
The Scandinavian models are welfare states with capitalist economies. There is no socialism here except for Marxist influences within the Social Democratic parties. Many of the views held by Social Democrats can be inline with most socialists/communists, but the economies of those countries is not socialism.
Anarchism is not a society without order, but one without a state. Concepts like Federalism and Confederalism are popular among anarchists. Famous examples also include Catalonia and today's Rojova. Anarchist societies simply see the state and capitalism as oppressive, and reject all hierarchal relationships.
Communism calls for the abolishing of the state. The Soviet Union and China are not, and never were communist societies. This is a very common straw-man. Do not equate strong governments, regulation, or centralized command economies with anything related to communism or socialism.
Don't confuse communists and socialists for being against democracy because a few transition states claimed to be communist/socialist. The DPRK claims to be democratic yet we clearly don't consider them any sort of democracy.
People are abusing the "No True Scotsman" Fallacy if they claim communists use it to say that the USSR and China weren't (aren't) communist. This is an abuse of a generally helpful logical fallacy that can otherwise be used to organize arguments. If you know the history, kindly explain it to them so they will understand.
Please be informed of these before continuing an argument. It makes a lot of arguments shorter and less riddled with misconceptions. Cheers!