I think Haunter's answer is spot on, but I'd like to draw out some clear differences b/w Fascism and Communism.
It's also got to be made clear that most Communists throughout history thought they were fighting for a MORE democratic, just and fair world than what capitalism could offer. Of course, what resulted in Russia turned out to be an abomination to Marx's views, and much of what has considered itself a "Communist" regime since then has simply meant dictatorial regimes following Stalin's path to development. There are also incidents of the far left deciding that inhumane methods may be necessary to eventually achieving a humane society (i.e Trotsky). But I'd like to step back before all this, to Marx and to the original ideal of Communism before it was polluted by the circumstances of history.
So if we go back to what Communism meant before Stalin, and before the world had access to information about Stalinism, it meant a total democratization of the economy and a classless, nation-less world.
Therefore:
1. Communists are INTERNATIONALISTS, they stand for the abolition of nations. They think that nations serve to undermine global class solidarity and undermine the possibility of world revolution.
Fascists are NATIONALISTS, usually the most extreme ones. They don't want other nations interfering with their own, particular, national values.
Hence, Lenin opposed WW1, he considered it an imperialist war only benefiting the capitalist classes. One of Hitler's biggest ideological planks was that he thought Germany had been shamed by WW1 and the treaty of Versailles, he wanted to fight it again!
2. Also, Communists always OPPOSED RACISM and racial inequality. They participated in the civil rights movement, they campaigned for indigenous rights around the world. Fascists often stand for RACIAL PURITY, for racial particularism and even for open genocide!
3. Communists are against CLASS and social hierarchy. They want the working class to be in control of everything! They think the state will "wither away" as it wont need to perform its primary function anymore--enforce class domination.
Fascists may celebrate the working class as contributors to the national good, they may even give them a better material existence than they had under liberal capitalism, but they are for an AUTHORITARIAN DICTATORIAL STATE. They most definitely don't want workers to be in control, they want the state to be in control and they want to rule the state.
This might go some way to explaining why during the 20s and 30s, most countries that had growing Communist and Fascist movements saw them openly fighting each other in the street!
It's true that the Communist movement defined everyone as a social fascist during the early 30s. This was a ridiculous idea and proved to be an immense failure. But the directions were coming from Stalinist Russia, which soon afterwards decided to make a pact with Hitler, demoralizing much of the international communist movement. I think this says less about Communism as an ideal, and much more about just how far removed Russia was from that ideal.