Communism is one form of socialism.

The ruling elites own everything and control the means of production directly.

To run a business you need to be a party member and the party dictates how your business is run.

Fascism is communism with one extra step.

To run a business you still need to be a party member or have one working with you. You do get to however manage your business as you see fit though still have the state ruling party as your boss.

Fascism is the Merger of state and private. Cartels.

You can see it in the film Schindler list. Oscar had to join the party. He could buy a factory with his own and investors money but once he did the state bought all his goods. Told him what to make. But he could operate the business his way to a certain extent. Oscar was the nominal owner the state the defacto owner of the means of production

To lolbertarians who think having taxes for roads are fascism they're the same thing.

While others could explain it far better than me I'll give it a shot.

Communism and Fascism, specifically Fascist Corporatism (the economic system of Fascist Italy) are both collectivist ideologies and have similarities, but both their motivation, and methods could not be more opposed.

I can suggest reading some Oswald Mosley and Mussolini for different takes on the idea of corporatism, which actually predates fascism by quite a bit as it originated with Saint Thomas Aquinas in the 1200s.

The basic idea is that the economy is organized into corporations which are expected to act as organs of the body (corpus means body, and this is where the name comes from), their purpose is to enrich the nation as a whole first, profit is secondary to providing for the needs of the people. For example if many people were dying of opioid overdoses the state would jump in and say "ok (((sackler))) family, you clearly don't have the nation's interests at heart, because you value your profit more than not killing people you don't get to do pharmaceuticals anymore. One important part is that Multinational corporations would need to be abolished, as a corporation existing in multiple countries creates a conflict of interest, just as the same organ cannot serve two bodies equally neither can the same corporation serve two countries equally.

It is important to note that personal&private property both exist under corporatism.