How are the two files in the generated SSH key pair used?
Both files are public and should be placed in authorized_keys.
authorized_keys
Keep id_rsa secret on the client and place id_rsa.pub in the server account's authorized keys.
id_rsa
id_rsa.pub
Both files belong only to the SSH server and are unrelated to the client.
Keep id_rsa.pub secret and copy id_rsa to every server.