Liberalism and the left are often referred to interchangeably and they frequently work together for similar things. There is a difference especially when we talk about democratic socialism and even social democracy. Pointing out the differences doesn't mean liberals and leftists should be enemies. In fact the left plays a crucial role in activism and grassroots organizing efforts for social change that liberals support. Moreover radical demands and ideas often become modified into liberal public policy. Nevertheless we need to recognize the differences to better understand debates around capitalism, economic inequality, and the Presidential candidacy of Bernie Sanders.
Democratic SocialismEmphasizes the need to work peacefully within the democratic process to bring about collective ownership of the means of production. Furthermore once capitalism has ended it uses democratic means to make economic decisions and preserves certain democratic freedom unlike totalitarianism which tries to control and repress every aspect of individual life while not allowing any dissent. Many democratic socialists would argue that real socialism has never existed anywhere because they reject the abuse and excesses of communism whether in the former Soviet Union, Maoist China, or the Third World. But the also tend to think that Western Europe's Labor and Social Democratic parties do not go far enough.
Social DemocracyEmphasizes the values of freedom, equality, and social solidarity. It may seek to realize democratic socialism at some point or accept capitalism while striving for the values mentioned here. Social Democracy has profoundly impacted Western European countries like the UK, France, Germany, Norway, Sweden, and Denmark. It has kept much of capitalism with strong regulations, some state ownership, and a universal welfare state including free healthcare for all. They have used high taxes to nearly eliminate poverty, reduce wealth income inequalities, and preserve a large middle class.
LiberalismEmphasizes individual liberty. Things like equality, tolerance, and limited government within the rule of law uphold individual liberty in liberalism. Liberals want to prevent tyranny by controlling power exercised by anyone in society or government. Contemporary liberals unlike their classical forbearers are more supportive of government in society and the marketplace because they see private threats by capitalism as well as government to individual liberty. Liberals in this sense value economic regulation and more limited means tested welfare. Liberals are committed to the individual and private property so they want to control capitalism not abolish it.