socialism is the government owning the means of production; fascism is the private sector still owning the means of production, but with the government controlling it.
As an economic system, fascism is socialism with a capitalist veneer. The word derives from fasces, the Roman symbol of collectivism and power: a tied bundle of rods with a protruding ax. In its day (the 1920s and 1930s), fascism was seen as the happy medium between boom-and-bust-prone liberal capitalism, with its alleged class conflict, wasteful competition, and profit-oriented egoism, and revolutionary Marxism, with its violent and socially divisive persecution of the bourgeoisie. Fascism substituted the particularity of nationalism and racialism—“blood and soil”—for the internationalism of both classical liberalism and Marxism.
here socialism sought totalitarian control of a society’s economic processes through direct state operation of the means of production, fascism sought that control indirectly, through domination of nominally private owners. Where socialism nationalized property explicitly, fascism did so implicitly, by requiring owners to use their property in the “national interest”—that is, as the autocratic authority conceived it. (Nevertheless, a few industries were operated by the state.) Where socialism abolished all market relations outright, fascism left the appearance of market relations while planning all economic activities. Where socialism abolished money and prices, fascism controlled the monetary system and set all prices and wages politically. In doing all this, fascism denatured the marketplace.
http://www.econlib.org/library/Enc/Fascism.html