No. Both have a similarity in a basis in the marketplace. However, a free market is a special case in which there are no external controls on free economic action. Market economies may or may not have such influences, but are only contingent on some basis in the marketplace.
For example, the United States is a market economy. But with the degree of government intervention, it is not a free market economy. The closest in the world today is Hong Kong, but a pure free market is as hard to find as pure communism.
To expound further, this is a difficult question, as the common meanings of "free market", "market economy", and "true free market" are not what an Economist would define. That is, there is a disjoint between common usage and technical definition.
From an Economist's standpoint, and Market Economy is any one which uses the principles of supply/demand and open trade to transact economic activity. As such, the world has come to the point where all countries use a Market Economy.
However, inside the category of Market Economy are a large variation in the level of three factors: government regulation, government ownership of industry/infrastructure, and government social programs. An Economist would stay that having more than a very minimal level in each category would move that economy into the Mixed Market Economy category. As current governments have high levels of regulation, some minimal level of government ownership of industry/infrastructure, and at least moderate levels of social programs, it's hard to classify any current nation's economy as anything but a MME. That is, from the Economist's perspective, there are no Free Market economies, let alone True Free Market economies (except in places where there is no functioning government at all, such a places undergoing civil war or in a state of anarchy).
To be clear, from an Economist's standpoint, a True Free Market Economy is a form of Market Economy where the government provides only two functions: a single legal common currency, and adjudication of contracts. A Free Market Economy is one where the government would add some lower level of regulation on allowable economic activity, such as pollution controls, or prohibition on certain abusive economic activities (i.e. market manipulation or abuse of monopoly status), but does not engage in either ownership of industry/infrastructure or any government-sponsored wealth transfer (e.g. social programs).
So, really, we are splitting hairs. Given that all countries are running an MME (according to an Economist), when ordinary people say "true free market" or "free market", what they are generally referring to is those countries with lower levels of regulation/ownership/social welfare than other countries. In common usage, these terms are relative, not absolute.
This can easily be answered without large paragraphs. A free-market economy is called Capitalism. A market economy... It isn't really a term. It is the Same as a Free-market economy. The people closest to this would be the Hong Kongese but even yet, they are what the U.S is: a Mixed Market Economy. Period.
The US, Japan and Germany are all market economies. In a traditional economy. In market economies, economic decisions are made by individuals.
Almost every country has a market economy; North Korea still has a command economy. WRONG^^ U.S. is rumored to be a market economy, but there are not pure market economy.
Free- enterprise system
yes, it has a market economy.
Command economy, market economy, and traditional economy. The United States of America is a Market economy.
yes Russia does have a free market economy after their new president got elected
The US, Japan and Germany are all market economies. In a traditional economy. In market economies, economic decisions are made by individuals.
yes and no... if you want to buy stuff you go to the socialist market then otherwise i think it's the same.
No, a command economy is where the central govt. controls everything. A market economy is where the govt. trades, buys, and sells products from different countries.
Market Economy.
Almost every country has a market economy; North Korea still has a command economy. WRONG^^ U.S. is rumored to be a market economy, but there are not pure market economy.
a market economy
No, china does not have a market economy!
market economy encoursae
Market economy
yes, it has a market economy.
Free- enterprise system