The United States economy has variously been described as "free market," "capitalist," and "mixed." The apparent confusion here is caused partly by the differing terms and approaches of different economic schools of thought. The term "capitalist" has its origins in Marxism and tends to be used by those who disapprove of the United States system.
The approach of classical economists has generally been to see all the economies of the world as existing on a continuum from free market economies to command economies. In the former type of economy, everything is determined by the market; in the latter, everything is determined by government. It should be clear even from this summary that there is, in practice, no such thing as a pure free market or pure command economy in existence. Every government in the world exercises some control over fiscal policy, taxing its citizens and spending their money for the common good. It is difficult to see how a pure free market economy would arrange military spending, for instance.
Similarly, there is no such thing as an absolute command economy. Every system in the world contains some element of private enterprise, however much regulation the government puts in place. The truth, therefore, is that all the world's economies are mixed economies, but this insight is not very illuminating. This is why many people call the United States economy a free market economy, because it is closer to the free market end of the spectrum, having less government regulation than most other economies in the world.