CDC would only concern themselves with transmittable prions, so it makes sense that they'd not list cancer, it's a little different (and might not be considered a prion from a purely medical perspective, I'm bio, not medicine). But it sounds like they're only listing mad cow too. I'm pretty sure mad cow covers it then.
Basically, when a protein malforms and causes a disease, it's called a prion. Since these won't be cooked out, they're dangerous. AFAIK, this only includes mad cow, but I've heard (but not verified) a similar malady in sheep that is transmitted through the lungs, so haggis would be out. Diseases caused by live parasite will be prevented by cooking, this includes most animal diseases. Once the animal is butchered, age can allow for certain bacteria to build up poisons that can't be cooked out. The most notable of this class of disease is botulism, which is harmless as a bacterium, but releases botulinum, which is a paralytic poison. Botulinum, you might be interested to know, is the active ingredient in botox.
Unless you want me to expound how a string of amino acids becomes a protein, you've got as much knowledge as I can give you about prions.