If one way SSL is used (Server Certificate authentication) then data sent from client gets encrypted using Public key of the server certificate. So privacy protection is availab
In SSL, two things happen:
First, a session key is negotiated using something like the Diffie-Hellman method. That generates a shared session key but never transmits the key between parties.
Second, that session key is used in a normal symmetric encryption for the duration of the connection.
SSL does use public/private in one way, because an X509 certificate is used to identify at least one end of the connection. Those certs are signed using an asymmetric key pair.
Extracted from How can SSL secure a two-way communication with only one key-pair?