The idea of a free market is central to both America's concept of itself, and to its prosperity. A truly free market is a fair and level playing field in which individuals can buy or sell as they please, and in which creativity is encouraged as inventors and businesses offer new products, or offer old products at new prices. In this gigantic experiment, people sometimes choose to take risks - a new gadget make become popular, selling well and making its manufacturer rich; or it may sell poorly, and the investors lose their money. People also have the freedom to decide not to take risks; they can choose to manage their money more conservatively, excluding the possibility of sudden wealth, but also excluding the fate of sudden poverty. A free market generates prosperity; even when a business closes, as some inevitably must, they will be replaced by others - as long as the market remains truly free - who will offer employment.
But the notion of a free market is an internal one, a domestic concept: it refers to businesses competing with each other inside a country.
Quite different is the phrase 'free trade' which refers to international trade. This phrase indicates a movement to reduce or eliminate tariffs - import taxes. In theory, if nations eliminate their import taxes, then we would have a free market among nations. But this doesn't happen in practice. First, few nations actually eliminate their tariffs; they may reduce some, eliminate others, and leave others in full effect. Secondly, even if tariffs were totally eliminated, other factors prevent global trade from being a level playing field. Different national economies are conditioned by internal variables - regulations and subsidies - which cause price distortions in their products.
While a free market is generally desirable, and almost universally desired, free trade is much more problematic. This is seen in the long history of trade between the United States and China. Initially, China didn't want free trade because cheap, mass-produced American goods undercut China's domestic manufacturers. Later, the very opposite situation occurred, and now it is America who would rather not have free trade with China.
Despite what nations may want, they sometimes end up with something else, because other diplomatic factors may force countries to engage in free trade when they would rather not do so.