Ok this is tedious, socialized typically implies a higher level of government involvement (benefits, regulation, subsidies etc.) and often nationalization (like that socialist mexican oil platform that just lit the gulf on fire) than say a more free market economy democracy. Yes, technically you can have a socialist democracy. (Depending on how you stretch the word “democracy” you could have a democratic anything) However, in socialist democracies it is rare for companies to enjoy similar protections from government interference as the individuals do (and often the individuals are interfered with more as well). So a democratic company is a company in a nation whose democratic politics result in protections of the companies as well as the people. All political systems are fundamentally economic systems, lets not be naive.