Why git authentications works through SSH keys?

Question in the title, but let me detail more. Excluding the ID/Password method on git CLI, we generate a SSH key and add the public key to the remote server. Why don't we have SSH-less public-key cryptography methods? We are not even connecting to remote a machine's terminal, we don't even need to connect a remote machine's terminal (do we?), so why is it named as SSH key? Is it just about naming convention, or something else? What is the history behind that?