The primary difference between capitalism and socialism is that capitalism promotes innovation and personal pursuits, while socialism promotes societal fairness and equality. A capitalist economy accepts that income polarity is a reality in order to motivate high performers to develop new ideas and products for personal gain. A socialist economy tries to balance wealth through policies that ensure each person has an adequate amount of income, food and supplies.
The holder of economic control also varies. In a capitalist system, private companies and individuals drive the economy by developing successful businesses, making money and paying workers. In socialism, the government controls the economy by allocating resources and coordinating the redistribution of wealth.
One advantage of a socialist economic is that unemployment is typically very low. The government assigns jobs to ensure people aren't out of work. In capitalism some level of unemployment is inherent based on the requirement of employers to have educated, experienced and qualified workers for each position.
One of the most important distinctions between the two economic systems is control of pricing. Capitalism is largely a pure economy, which means it has few government regulations, and companies, with influence from consumers, control much of the market's pricing. In socialism governments control pricing through price ceilings and price floors. Government pricing tends to cause shortages or excesses in supplies.