A socialist economy is an economic system where the government controls the major means of production but property and other businesses may be privately owned.
A communism economy is where the government controls all aspects of production and how resources should be used and what services will be provided. A capitalist economy is where there is little interaction from the government controlling production and property but that the business itself can determine their production levels. A socialist economy is the mixture of the two systems and allows more freedom for privately owned businesses.