Grass fed cattle are raised on an open range and eat grass which is natural to them - they're also kept on much larger spaces than most corn fed cattle. Corn fed cattle are usually held in small lots and fed corn feed to make them big and fat as fast as possible. The difference is that corn is not naturally the whole cow's diet, and nor is confinement. So these cows don't get sick they're pumped full of antibiotics for preventative care, even if they're not sick. They're often also fed hormones to make them fatter quicker. In the end the human ends up eating the meat that still has antibiotics and synthetic hormones in them. Grass fed cattle are less likely to have these issues and even if they do they're still being fed what is natural to them and some people claim that makes the meat tastier. I don't know - never been fond of beef.