I agree with the terminology being a problem. Regarding private key public key encryption, I think the public key should be called the "lock" since people use it to lock data they want to send you, while the private key should be called the "key" because you use it to "unlock"(decrypt) the data.
But this messes up when you use the same terms for other uses of public/private keys such as authentication. Still, the terms could provide a better mental model for people new to it to understand.
That breaks down when you use your private key [aka the "key"] to encrypt/sign something when you send it out. It proves it came from you because your public key [aka the "lock"] can decrypt it.
But this messes up when you use the same terms for other uses of public/private keys such as authentication. Still, the terms could provide a better mental model for people new to it to understand.