A market is an environment in which the action of trade between a buyer (consumer) and seller (producer) occurs.  Trade is the exchange of goods, services, or ideas, and in modern times is often executed via an intermediate store of value such as currency.

A free market is an environment, absent of physical force, compulsion, or coercion, in which the action of trade between a buyer (consumer) and seller (producer) occurs.  Such force is often applied in subtle ways, but results in interference in the terms of trade. The source of such interference is the action of other individuals--typically other buyers, sellers or governmental officials--including those participating in the trade.  Thus, trade in a free market is strictly voluntary, and occurs only as mutual cooperation amongst individuals.

Note that the restriction of force in the definition of a free market does not establish the legality of such action, nor does it set into law any terms of enforcement.  This is the province of law and is established independently through political systems of governing.  Coercion and physical force can take many forms: assault, murder, theft, fraud, or vandalism—but the legality of such actions is enforced by a system of law, not a system of economics.

This single distinction--the restriction on the use of physical force, compulsion, or coercion--forms the only fundamental difference between a market, and a free market.