If you want to get bogged down in detail then Socialism is a great place because its like an onion in a way, lots of differing layers & levels but its all onion just the same.

There's varying strains of Socialism before & after Marx going back to the French Revolution and even earlier but after the Marx/Engels efforts its come to broadly mean (to most not all people) the opposition to Capitalism and the advocating for an alternative to capitalism which includes the state ownership of the means of production. Some times the words state & workers are interchangeable but it means no enterprising entrepreneur is really going to have a good chance of building a small business into a large business.

For a nation to be a proper Socialist Nation, so far its not been tried without being a totalitarian state.
That means harsh authoritarian rule. There is the seemingly glib but still rather accurate idea that socialism can only work until other people's money last & then follows brutal force and killings.

Then there's communism. Like socialism, it opposes capitalism. Like socialism it will need brutal force to survive. It will centralise power to one party, it will make even less concessions to free markets than Socialism and it will repress any dissent. Communism is more about all wealth & production controlled by the state, Socialism more along the lines of equal distribution amongst the people.

Its all hair splitting to some and there's a lot of strains of either. But again, its what Socialism, Communism, Marxism all share that's important.

They oppose capitalism
They oppose free choices of the individual to the point where the state is more important than any individual or group of individuals. (Some will argue groups of any individuals will be dissuaded or banned)
They do require lots of other people's money.
They oppose the free market
The State rules over everyone, it needs authoritarian/totalitarian rule to survive

So what is the difference between that and Nazism/Fascism?

A lot and not a lot.

look for the things in common & the differences. Socialism & communism is seen as the left, Nazism is seen as the far right. Are they?

Well Fascism was really firstly formed by Giovanni Gentile and from there strains developed.
But whilst Socialism was based on being anti class & then forming one class (in theory until the ruling class then develops and takes control) Nazism was based on extreme Nationalism & Race.

Whilst they spring board from different points, they share commonalties

They oppose capitalism
They oppose free choices of the individual to the point where the state is more important than any individual or group of individuals. (Some will argue groups of any individuals will be dissuaded or banned)
They do require lots of other people's money.
They oppose the free market unless the market is benefitting the chosen few.
The State rules over everyone, it needs authoritarian/totalitarian rule to survive

Both Socialism/Communism and Nazism/Fascism are more than willing to kill their own people to keep the system pure.

The accepted "Western" model of nations will allow free movement, citizens have individual rights, they can work, buy & sell as they choose. They can profit & after paying tax can do whatever they want with their profits no matter how big or small the amounts are. Migration is allowed, racism is banned, they are free market based.

So its pointless arguing whether Fascism is of the left or the far right. Both need brutal totalitarian rule, the power to take anything & everything from whomever the state dictates. Both are horrid political forms of brutal tribalism that eventually will cost lives to sustain itself.

In the free market country no one is forced into re-education camps because of race, religion or political views. The Marxist/Fascist countries...standard operating procedure.

Here's the saddest point, which is considered worse these days Communism or Nazism?
Easy, Nazism. They caused the holocaust, tried to conquer the world, caused the death of many through systematic genocide.

But going wider, who killed more, Stalin, Mao or Hitler & who got demonised the most?
Well the numbers are irrelevant but because all caused the death of millions, the real question is, why aren't Stalin & Mao not demonised as much as Hitler?

Easy. Hitler was defeated. All were brutal genocidal regimes.
No one asks how many people a British PM caused because they haven't had an totalitarian regime committing war, mass murder & genocide.

In fact if you're going to put Stalin, Mao & Hitler in the same boat (you should) you probably should put North Korea's Kim dynasty in there, plus Pol Pot, Cuba, Venezuela...

The argument should not be "Is Nazism of the left or the right?"
Its probably like Stalinism, Marxism, Socialism, Communism et al in that they're brutal anti free market murderous totalitarian regimes of death, heresies of humanity.

There is no safe harbour or perfect high moral ground for any form of government, however the western capitalist one doesn't build re-education camps, dispossess individuals assets, commit mass murder and control all means of production.

Capitalism isn't perfect, but its non oppressive and murderous.

If its not a western based, free market based, individual rights preserved type of society, its either murderous or soon will be.