I agree with what you are saying but socialism is older than Marx. The French Revolution was a socialist revolution. That is why it was a blood bath. It goes back further than the French Revolution. I actually don't know when it was first tried. I am not sure but I don't think anyone has written down a definition of socialism until Marx came along because Marx is the major influence in all socialist, communists movements and was a major inspiration of Hitler.
Fascism is based on socialism but I just found out recently what Giovanni Gentile was trying to accomplish when he created fascism that Benito Mussolini adopted. He allowed people to own their own property, he allowed businesses to remain private enterprises. But the difference between classical liberals (who today are modern conservatives) is he believed in the supremacy of the government over the people. He referred to the government as being "benevolent" but as we can clearly see that when you give all political power to the government they quickly turn corrupt. In Hitler's case he started off corrupt and just got worse as he accumulated more power. He was kind to some people but extremely cruel to nearly everyone else.
The end result of fascism, despite it allowing private ownership, is exactly the same as all other socialist regimes where private ownership and private property rights are not allowed.
Also fascism from the start relies on a large centralized government just like what Democrats want.
Democrats are far closer to true fascism than anyone on the right. The right are the true Anfifa but unlike the actual Antifa we also don't want communism. We don't want any kind of Statism, collectivism or any other kind of authoritarianism because all political power resides in the hands of the individual and none of it in the state. We The People tell the state what it can and cannot do. And we just want the Constitutional Republic that our founding fathers gave us and we want freedom for all.