We are better off pointing to the distinctions in order to conclude upon the similarities, rather than the other way around which will be rejected off-hand. The similarities have been well described here. Some distinctions:
- Nazism/fascism maintains private property;
- Nazism/fascism is nationalism whereas socialism / communism pretends [emphasis important here] to be borderless;
- Socialism/communism is a means whereas Nazism/fascism is an end.
We unfairly discredit our detractors and get no where with them if we ignore these distinctions. Rather than saying they are one in the same, I prefer to get the left itchy on its similarities to fascism by pointing to those aspects of the modern left which are more fascist than communist. It's easy for the left to deny being communists; they're not, no matter how much they are, for they haven't the power to be. However, they have undeniably approached the fascist state: nationalism.
The nationalist wants a public/private partnership. This is best expressed in Latin American dictatorships where business is an adjunct of government, just as it was under Hitler in Nazi Germany (Mercedes-Benz was a prime example). The Americans approached this earlier, in fact, during the progressive era, when Teddy Roosevelt's "New Nationalism" had the country headed towards a government-business partnership that would have yielded permanent monopoly status to the likes of Standard Oil and U.S. Steel.
Socialism/communism wanted the same thing but with public ownership. The progressives/nazis/nationalists allowed for private ownership, but under government guidance. We are far closer to nationalism than communism.