Socialism was brought up intially because many existing economic systems in the 19th century may have differentiated from opressive, pre-enlightenment governments but really didn't do much to help the lower class (social "have-nots". A socialist would want a safety net for the poor so people wouldn't be on the streets getting sick and starving. They would pay for this safety net by allocating some of the money from the people who have a lot more than they need to the people who have a lot less than they need. Some forms fo socialism want commune-like work places, others call for direct state-control. Some socialists nowadays strive for a mixed economy.
A Marxist scoffs at how exactly many socialists intend to reach socialism. Marxism and Leninism tells us the middle class must be killed off in a violent revolution to end all revolutions. Afterwards, Marx says that only then can socialism be established and have the society as a whole would control places like factories. Eventually, once the workers are able to run an economy without a government or private sectors, the state will wither away! War will be ended, no one under communism will fight because there are no more social classes that make some people look better than others.
Under both systems, the community is more important than the individual. Branches of socialists, such as people who call themselves social-democrats, insist on step-by-step democratic reforms toward socialism. Some socialists condemn communism because ethics play a role in killing off the middle and upper class. Many communists will often say that the Utopian Socialists, the Utilitarians, or the Social Democrats are bound to fail because the middle class will become corrupt and selfish much as they had in the French Revolution of 1848. The communists say the middle class will never give to the lower class in a socialist economy, so their solution is death in the name of the working men of all nations.
Me trying to explain to people the difference between radical left-wing Marxists and non-Marxists