Client-only packages include the components, which implement only the client side of the corresponding protocols. Client-server packages include the components suitable for both client-side and server-side of the communication.
Client-only package can be used in server environment, as long as the server acts as a client, when using the selected protocol. For example, you can use SFTPBlackbox client-only package to transmit the files from your server to some remote server, as long as your server initiates SFTP connection and acts as an SSH/SFTP client.
See the scheme for explanation: