Correct. It's a common way in which socialists try to pervert the definition of "capitalism" in order to make subsequent strawman arguments against it.
The real distinction is very straightforward: "Socialism" is the state ownership of the means of production and "capitalism" is the private ownership of the means of production.
Private ownership implies a free market economy.
Perhaps private ownership is the basis in law for “capitalism”. I to prefer the free market (non- interference in markets by the state). It incompasses the private ownership of means of production and also the disposition of those goods. Taxes of any sort are also interference in the market. The owner of the goods should be able to sell for any price, to any person that the owner wishes.
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I tend to think of it as "ownership" meaning "exclusive right to control", which would include making or rejecting proposed trades.
Properly understood "capitalism" and "free markets" are just two sides of the same coin.
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