From Wiki
"Democratic socialism (also known as evolutionary socialism) is a political philosophy that advocates political democracy alongside social ownership of the means of production, with an emphasis on self-management and democratic management of economic institutions within a market or some form of decentralised planned socialist economy. Democratic socialists espouse that capitalism is inherently incompatible with what they hold to be the democratic values of liberty, equality and solidarity; and that these ideals can only be achieved through the realisation of a socialist society. Democratic socialism can be supportive of either revolutionary or reformist politics as a means to establish socialism.
In the term democratic socialism, the adjective “democratic” is used to distinguish democratic socialists from Marxist–Leninist inspired socialism which to many is viewed as being non-democratic or authoritarian in practice. Democratic socialists oppose the Stalinist political system and Soviet economic model, rejecting the perceived authoritarian form of governance and highly centralised command economy that took form in the Soviet Union and other socialist states in the early 20th century."
But I think the Democratic Socialism of America is more along the lines of Social Democracy because
"Democratic socialism is distinguished from social democracy on the basis that democratic socialists are committed to systemic transformation of the economy from capitalism to socialism using governmental means, whereas social democrats are opposed to ultimately ending capitalism, and are instead supportive of progressive reforms to capitalism. In contrast to social democrats, democratic socialists believe that reforms aimed at addressing social inequalities and state interventions aimed at suppressing the economic contradictions of capitalism will only see them emerge elsewhere in a different guise. Democratic socialists believe that the systemic issues of capitalism can only be solved by replacing the capitalist economic system with socialism—i.e. by replacing private ownership with collective ownership of the means of production, and extending democracy to the economic sphere."
Wikipedia is such a useful tool