One is a form of government, one is an economic system. A democracy can vote to have socialist economic system. It has been done in part in Europe. They tend to go together because they share a common theme of individual freedom of choice. That theme is tempered in most democracies by concern for minority rights and the society as a whole. No country respects individual freedom so much that it places no restrictions on harming others. Abuses of unfettered capitalism are well documented. That experience is why no absolutely free markets exist in stable democracies just as no true anarchies exist (at least as long term functional societies).

Regards,
Mark