Mad cow disease is Creutzfeld-Jacob's disease (CJD) in humans, kuru is a different prion. But don't worry about it, would-be cannibals: it's only transmitted through eating infected human flesh, not human flesh in general. As long as cannibalism isn't common in your society, the prion will be rare in turn.
No, all are the same basic disease, but with different routes of manifestation. All center around the same protein, PrP.
https://ind.ucsf.edu/research/mad-cow-scrapie-kuru-cjdhttps://en.wikipedia.org/wiki/PRNPKuru is specific to endocannibalism of infected individuals as the route of transmission.
MadCow is specific to the consumption of bovine meat that originated from animals with bovine spongiform encephalopathy.
CJD is an inherited form, caused by a mutation in the gene which increases the incidence rate of misfolding/dysfunction.
The mechanism of the disease process involves the fact that misfolded versions of the protein (the "infectious" form) actively promote the misfolding of additionally produced copies of the protein, which is what leads to the buildup of the protein in cells, and what ultimately causes cell death.
The confusion you have here, is that ANIMAL versions of this gene are different from the human versions, and there is less capability for animal versions of the misfolded protein to influence the folding behaviors of human versions.
See for instance, why it is perfectly OK to eat mutton from a sheep that suffered from scrapie, but not from a cow that suffered bovine spongiform encephalopathy. (And, since we are talking about madcow-- why cows cannot ingest meat from sheep that suffered from scrapie.)
The route of contamination in the UK madcow epidemic went down like this:
Scrapie infected mutton --> Humans == OK, No problems.
Humans thought, "Safe for us, should be safe for cows too; Inexpensive protein enrichment for cattle feed!"
Scrapie infected mutton --> Cattle --> Humans
Except then the sheep version of misfolded prion protein was sufficiently similar to bovine version, that it caused bovine encephalopathy, and the bovine version of the prion was sufficiently similar to human version that it caused kuru like symptoms, and variant CJD.
Kuru and MadCow are really the same disease (Misfolded human prion protein, from food), but from different initial vectors. (Kuru comes from eating people; MadCow comes from eating beef.)
They are both functionally the same thing as CJD (which is genetically originating.)