No mad cow disease is quite literally Creutzfeld-Jakob disease, it's vCJD, with v standing for "variant", to specifically distinguish it from "normal" CJD which is heritable. usually CJD is caused by a specific mutation in the human prion protein that renders its susceptible to turning into plaques; vCJD does not require this mutation and happens in wild type protein, though it's unclear if other heritable factors can contribute to susceptibility.
(I worked in a protein plaque lab and did a small, inconclusive experiment about cross species CJD transfer)
I don't know why the CDC is saying that, it's just flat out wrong unless the CDC has a really stupid definition of "related".
It's related. They both involve the same protein. If you get a bone marrow transplant from someone with CJD, you will get "vCJD". Presumably also if you eat the brains of someone with CJD. The differential between the two is age of onset.
(I worked in a protein plaque lab and did a small, inconclusive experiment about cross species CJD transfer)