The difference is that "the other terrible stuff", at least the infectious stuff (not so much the hormones, antibiotics and other trash they feed most cattle these days–but that isn’t limited to ground meat), can be avoided by (a) cooking your burgers thoroughly OR (b) grinding your own beef as I do. This is because the contamination, disgusting as it is to think about, is mostly from contamination by feces in the slaughtering process. After the meat is butchered, this material remains on the surface and, in the case of whole cuts, can be washed off–if necessary by YOU (or ME) before the meat is ground. But if the meat is ground before we get it, the contamination gets mixed in and cannot be removed–but the germs can be killed by cooking IF all of the burger–right to the center–is cooked to a high enough temperature.
When it comes to mad cow, there’s not much the consumer can do. The prions that cause it are NOT killed by cooking. Again, grinding your own meat may help by avoiding (or minimizing) inclusion of the nervous system tissue that the prions mainly call home. But there may be small nerves in even good cuts of steak and I don’t think it’s certain that prions cannot exist in any other tissue.
BT, M.D. (but not, by any means, a mad cow expert)