Interestingly enough Marx used Communism and Socialism interchangeably in fact socialism is a phase on the path to communism.
Satisfy yourself and look up the definition of Socialism Merriam Webster says:
Full Definition of SOCIALISM
1
: any of various economic and political theories advocating collective or governmental ownership and administration of the means of production and distribution of goods
2
a : a system of
society or group living in which there is no private property
b : a system or condition of society in which the means of production are owned and controlled by the state
3
: a stage of society in
Marxist theory transitional between
capitalism and
communism and distinguished by unequal distribution of goods and pay according to work done
If you paid for a college degree that gave you the definition you used you were cheated and should look at everything you learned with a grain of salt.