Do free markets impose a form of rationing?

Advocates of free markets often observe that government controls over medicine, food, gasoline, and other consumer goods result in rationing, whereby government bureaucrats decide who can obtain the goods necessary for life. In response, I've seen people argue that the free market imposes its own form of rationing, whereby a person's wealth determines whether he can obtain the goods necessary for life. This parallel seems wrong to me, but I can't put my finger on the error. So what's the difference between "rationing" in markets and "rationing" by governments?