Still prompted for a password after adding SSH public key to a server

Extracting the certificate and keys from a .pfx file - IBM

PREREQUISITE: Ensure OpenSSL is installed in the server that contains the SSL certificate. ... You will be prompted to type the import password. Type the password ...

Is using a public-key for logging in to SSH any better than saving a ...

As you can imagine, in the first case the password is actually sent to the server (unless SSH would use password challenge response), in the ...