The word "socialist" has been widely used by people of very different political persuasions. In its most basic and most broadly understood form, the term denotes a political and economic system in which private property has disappeared in favor of communal property, where ownership of all value has become socialized instead of remaining privatized. Thus, for example, Saint Simon, Proudhon, Fourier, and Owen used it to connote a system in which there was no private but only communal property. Karl Marx and his collaborator Friedrich Engels appropriated this term and agreed that socialism was to be a system in which there would be no private property which to Marx and Engels -- just like to the aforementioned -- was the origin of all inequality, injustice, and evil. But in contrast to the previous users of the term socialism, whom Marx and Engels derisively called "Utopian Socialists," Marx and Engels believed that their much more sophisticated analysis of history as well as social and political developments -- buttressed in their detailed knowledge of the writings of German, especially Hegelian, philosophy, and British political economy -- warranted the self-serving sobriquet "scientific" meaning that their concept of socialism (as opposed to anybody else's) would actually happen and be the result of actual politics implemented by real people and their daily struggles and not be the result of wishful thinking and lofty philanthropy.
Marx and Engels used the words "socialism" and "communism" completely interchangeably, denoting in essence a system that would follow capitalism and be nirvana on earth. As they so beautifully termed it: It would lead from the world of each according to her/his abilities (which is the essence of modern achievement-based capitalism as opposed to ascriptive feudalism) to each according to her/his needs which is the essence of communism/socialism. Marx and Engels, of course, never really told us how one would get there, how one would transform capitalism and arrive at socialism. Thus developed a major debate following their death (Marx in 1883; Engels in 1895) as to how one could and should arrive at this nirvana.
In Western and Central Europe, most notably in Germany, Austria, the Scandinavian countries, even Britain (and to a much lesser degree in the United States) there emerged a huge movement anchored in the male industrial working class which called itself social democratic and which essentially believed -- and acted upon -- a framework that was to transcend capitalism in a gradual manner, meaning with no revolution and with no violence. In essence, this transition was to happen via the accepted legislative process in which these new social democratic parties would win elections, form the government, and install policies that would tame capitalism, improve the human condition and thus gradually move its way to socialism. Opposed to this were those who viewed this approach as far too lame and thus open to cooptation by powerful capitalism and who therefore opted for a violent overthrow of the existing system rejecting any accommodation with it and spurning any gradualism. The most powerful and influential advocates of this option were the Bolsheviks led by Vladimir Ilyich Ulyanov better known as Lenin. These two different paths to socialism became bitter enemies and remained so until the late 1960s, possibly beyond.
In the course of the late 1960s, there emerged something called the New Left which broke with the tenets of both, classical social democracy and communism and injected new dimensions into what henceforth connoted the essence of being left and progressive: small is beautiful replaced mega projects; the primacy of nature replaced the blind faith in technology; the salience of class being the most -- perhaps even single -- relevant collective was replaced by rivaling collectives featuring race, gender, third world movements and other forms of identity. It is at this juncture that there emerged something called democratic socialism that basically rejected the dictatorial and intolerant nature of communism; but also rejected the bureaucratic stalemate and boring institutionalism of conventional social democratic parties. Democratic socialists were creations of the New Left but rejected the violence of radicals like the Weathermen in the United States and similar groups in Germany, Italy, France and Japan and opted for an emphasis of a lived democracy in the process of emancipating all the disempowered be they women, minorities, the poor, nature. The most prototypical representative of democratic socialism was the late Michael Harrington who lived this credo's very tenet with every aspect of his political commitment and conviction.
Bernie Sanders hails from this world. He is the creation of the New Left on the East Coast who fully extols all the attainments of the New Deal and its Keynesianism (which are in essence social democratic) but who goes further in that he also wants to empower women, minorities, and other disempowered not only by matter of policy but also in their everyday treatment and more important still, in their dignity. Being a Democratic Socialist (as opposed to a Social Democrat) entails taking daily life and the power relations that inform it very seriously. It demands a democratic way of leading one's life on a daily basis and giving a voice to others. At the end of the day, Bernie Sanders wants capitalism "with a human face" to invert the words of the late Alexander Dubcek's never-fulfilled wish (crushed by Soviet tanks) of hoping for socialism "with a human face."