The main difference between a Fascist and a Communist state when it comes to the economy is that a Fascist state allows some ownership over the means of production ... but this ownership can be taken away at the whim of the government and you have only minor control over what you choose to produce.
Now, lets use a car company as an example to explain how a fascist economy works ...
In a fascist economy an individual (or group of individuals) may own a car company and they have some rights to produce cars that people might actually want to drive. Unfortunately, the government has full rights to step in at any point in time and take their company away from them and give it to their friends regardless of any standing contracts that exist, and the government has full rights to step in at any point and tell the company what cars to produce regardless of whether there is demand for those kinds of vehicles.
Edit: It should be noted that the Progressive movement of the first half of the previous century (which is the foundation of the ideologies that dominate the "Left Wing" of the political spectrum in most western countries) idolized fascist states like Nazi Germany; and shared many of the same scary policies about eugenics among other things.
