Anchor points for all terminological discussions on "capitalism vs socialism" :
1. "pre-market" implies jungle law i.e., the state of nature
2. "market" implies property rights,
ergo social contract,
ergo government
3. "capitalism" ( Louis Blanc, 1850 ) denotes the market effect :
"weak governments, regress towards pre-markets"
4. "socialism" ( Robert Owen, 1827 ) denotes the risk-management of markets, against regression to pre-market conditions
5. BONUS : "anarchy" can refer to 1. or 4.
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Discussion :
"from each according to their ability, to each according to their need", IMPLIES a market economy. The control i.e., communication system for abilities and needs, as contingencies for routing resources, is a market.
But this does not imply capitalism, which is that weak governance of the market is allowed to make the market ineffective.