Social ownership is private ownership--at least that's how I understand it. Here's another good article on the difference from The Atlantic:
In a social democracy, individuals and corporations continue to own the capital and the means of production. Much of the wealth, in other words, is produced privately. That said, taxation, government spending, and regulation of the private sector are much heavier under social democracy than would be the case under pure capitalism.The debate over Senator Sanders’ socialism is rich with paradoxes. Senator Sanders is not a proponent of socialism, and that is a good thing, for true socialism, whenever and wherever it has been tried, ended in disaster. Nor is America the bastion of capitalism that some make it out to be. In fact, U.S. taxes, spending, and regulation are quite high when compared to truly economically free countries. America’s is a mixed economy and so are Scandinavian countries’. It is the mixture that differs.