It is my understanding that EdDSA uses a slight variant of Curve25519 (typically used for ECDH), called Ed25519.
Given the same private key, are the differences between the two algorithms enough to make the resulting public keys different between X25519 and Ed25519?
In other words, if I'm writing code to generate private/public key pairs, do I need separate implementations for EdDSA/Ed25519 and ECDH/X25519?
Clarification: I realize that EdDSA mandates a SHA-512 step which ECDH/X25519 does not specify. I'm curious if the public keys are the same for the given input to the scalar multiplication step.