I got a .pk file, which inside I have a key that looks like this:
-----BEGIN OPENSSH PRIVATE KEY-----
CONTENT
-----END OPENSSH PRIVATE KEY-----
ssh -i key.pk user@IP
I got the following error:
-> Permission denied (publickey)
Yes, "Private Key" is what the abbreviation stands for. You are also correct in thinking that the file types are arbitrary; some organizations use different naming standards.
Your public key needs to be added to your user's .ssh/authorized_keys
file on the remote server before the key pair can be used. If you do not have the public key, the following command will retrieve a public key from a private key:
$ ssh-keygen -y -f private_key_file > public_key_file.pub