Nostr uses a different scripting for its public and private key pair generation than bitcoin, and it has nothing to do with bitcoin, it's completely agnostic.

You can use your public nostr key, your hex of your key or you can get NIP verified with a domain of your choosing and use a handle, clients can also do handle matching so in most cases people won't even use their public keys to engage with uses, only to sign in initially

Lightning doesn't have public and private key pairs btw, and it never has.

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