Democratic socialism means a democratic system with socialized (community/worker) ownership of production. Sweden is actually less socialist in terms of ownership as private firms are more prolific than corporations.* Of course, the decentralizing effect of shareholder systems is not useful if those shareholders are not workers (i.e. why US corps are frequently evil and undemocratic).
Democratic socialism can exist as a capitalist enterprise, I guess, but I don't think it has to. I support a more extreme view: socialism, that is democracy (not so liberal, but more communitarian) - democracy that manages production, which is owned by the people as a political asset, in the way that we share ownership over parks and government buildings.
So the distinction between state and worker/community ownership is based on how well that state represents the interests of its constituents. But this is why "state ownership" as shorthand is wrong for "socialism." Socialism relies on the premise that democracy cannot function properly alongside exploitative/.coercive capitalist systems, so that community/worker ownership needs to be represented as the foundation of the economic democracy.
This is just the same as the notion that local government should not be asking industry to ratify a convention to keep arsenic out of our drinking water. The industrial capitalists have no right to that veto. They also shouldn't be able to veto the right to basic living standards in an age of such incredible productive power.
*Sweden has robust labor institutions which are much more effective than corporate institutions at legitimizing policy based on consensus building, specifically by negotiation with private enterprise.