You're completely misunderstanding. I'm ONLY talking about the curve, and Ed25519 uses the same underlying curve as Curve25519, albeit with different representations.
Not my misunderstanding at all.
It would be better to say curve 25519 than Curve25519, because afaik the latter refers to a white paper for a ECC Diffie-Helman key exchange, which is a different purpose and more optimized than EdDSA which is for public/private key signing. Much more than a minor distinction (thanks to DJB for such premature optimization on the naming and confusion):
http://stackoverflow.com/questions/19147619/what-implementions-of-ed25519-existAlso for other readers and the original point of discussion, here is more on the advantages of EdDSA vs. Bitcoin ECDSA:
http://security.stackexchange.com/questions/50878/ecdsa-vs-ecdh-vs-ed25519-vs-curve25519