The essences of market economy are.
1. The sacredness of private ownership, (lately strongly damaged by the publicly owned corporate managers and banksters, who changed the aim of the companies from profit to the owners to the profit to the self nominated managers).
2. The existence of risk taking system, where every failure is punished and every success is priced. A permanent failure has to bring annihilation. (like in the case of Kodak, that refused to reinvent itself, so was destined to be annihilated).
3. Freely fluctuating product prices, that are too many times disturbed by subsidies initiated because of political means and bully kind of acts of the markets leading players.
4. Reward for excellence and punishment for the failure.
If to summarize the question what is the main difference between the economic entities run by government and the privately owned ones, the answer would be;
1. While the first is financed by money collected as taxes and to establish and maintain its activity this money doesn’t have to generate high yield the second needs to attract privately owned financial resources and this money can be attracted only by higher yield and what appears to be as lower risk.
2. If an entity run by government fails to attract sufficient demand for its product it still can continue its existence, while if the privately owned economic entity fails to attract sufficient demand, eventually it will perish.