Merriam-Webster definition of "socialism":
"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
2a : 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"
http://www.merriam-webster.com/dictionary/socialismAs stated, the central characteristic of socialism is the collective ownership of the means of production. A society, where private businesses exist, is not a socialist society. There has not been a single socialist state in Europe for over twenty years.
So, yeah: it would be more accurate for Sanders to call himself a social democrat rather than a socialist.