Socialism is defined as government or collective ownership of the means of production and distribution. Welfare benefits are not defined as socialism. Welfare benefits are just that extorted charity.
You're confusing communism with socialism. Communism calls for state ownership of means of production. Socialism calls for state control. Two different things.
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.