Why do people equate capitalism with a free market?

The term "Capitalism" has come to mean different things to different people. To some people the term Capitalism means what you refer to as "free market". It may be a result of the Cold War when the two spheres of power were one that supported "Communism" and another that supported "Capitalism". Given those two alternatives I will side with capitalism any day of year. Even the philosopher Ayn Rand (who wrote during the height of the Cold War) wrote about "Capitalism" as an "Unknown Ideal" and described it in a way that you would call a "free market".