What comparison between socialist and mixed economy?

socialist ,is where only public sector exist (perfect socialist),all of the production is distributed by the public enterprises ,generally motivates equality and unity ..while on other hand capitalist ,is where government doesn't interfere the working of economy (perfect capitalist),everything is decided or works on demand supply curve ,laissez faire economy ..people or capitalist (those who have capital or money ) decide what to produce ,how to distribute ,whom to distribute and how the surplus should be used .this economy is generally profit-oriented,which inspires or support polarization (rich gets richer and poor gets poorer).