As actually applied, most "Socialism" (e.g. in Europe) isn't, but has generally meant the central government not so much OWNS the means of production, as CONTROLS the means via various central production planning schemes like production control boards, or government control of a critical choke point in the production ranging from strict control of essential resources, labor allocations, or wage and price controls. The efficiency is much higher than in the 'Communist' states where the government both owns and controls the means of production, but still not nearly on a par with Capitalist productivity. The Nazis weren't particularly more Socialist than Brit Labour goverrnments in purely economic terms, though where they took their respective societies ideologically in other ways were obviously poles apart.
Mostly when people are talking about Socialism in the current political discourse, they are talking about the Euro version, not the pure theoretical version.