SocDems want to maintain private property as a social relation but have it tempered with strong labor. Basically they imagine that detente in the class war during the immediate post war period are the ideal form of social relations. They tend to completely ignore the material realities, like the USSR, that made the social relations specific to the post war period possible.
DemSocs actually want to change social relations in a radical way to abolish private property and create socialist social relations, but they believe the path to that is solely, or primarily, through the extant electoral system via the ballot box. In my experience most principled DemSocs are just naive as to the system they live in an move on to be anarchists or marxists; those that aren't just ScoDems calling themselves DemSocs.