A mixed economy can accurately describe virtually every economy in the world in 2017. A mixed economy is one in which there are elements of the economy controlled by market forces, and elements that the government plays a direct role in.
A pure market economy is one which the economy is run entirely by free market forces. The government has no role in regulation, subsidies, or any other action that would affect these forces. The success and failure of companies, the quantity of goods produced and the price of those goods, are 100% determined by the free market.
A command economy, on the other hand, is one in which the government manages virtually every aspect of the economy, and the free market is not allowed to naturally determine quantity and prices of any product. The USSR attempted to administer a command economy in its earlier years, and realized how tremendously complex and difficult this task was.
A mixed economy, such as those in the United States or China, is a broad term to define an economy that exists between these two extremes, where both government involvement and free market forces play a role in the economy.
