I'm currently developing an application using EC public key cryptography. However I'm a little bit confused by which kind of public key I should use for long term identity, Ed25519 or Curve25519.

As I understand, the curves are convertible ([0] & [1]), so it's not clear which one is better to use.

SSH and TLS use Ed25519 while Signal and NaCl use Curve25519.

Any pointer for which one should I use (or should NOT use)?

[0] https://curves.moderncrypto.narkive.com/BMafwQ5i/xeddsa-specification

[1] https://blog.filippo.io/using-ed25519-keys-for-encryption/