There is no real difference. The term "capitalism" is felt to be dissimilar from "free market", but no one is usually able to articulate a coherent difference. The central problem is that "capitalism" took on negative connotations over time and became deeply connected to Marxist/anti-Marxist rhetoric. At its core, though, it's still largely about ownership, even in Marxist critique or anti-Marxist defense. "Free market" is also a loaded term, it seems to signal being a libertarian, but generally refers to exchange restrictions; libertarians usually use "property rights" with respect to ownership issues. "Market" is fairly neutral, I think.

To take a stab at it, "capitalism" emphasizes the ownership elements of markets; "free market" emphasizes the exchange elements of markets; "markets" is just a neutral term, there aren't markets without ownership (rightful or not) and exchange (good or not). Neither "capitalism" nor "free market" deny exchange or ownership, it is merely a rhetorical emphasis; both specify the same set of objects, they just signal which features the author intends to dwell on.