A slave is one whose life is completely given over in service to a Master, without any personal rights.
A saint is one whose life is consecrated and dedicated by the Holy Spirit to serve God.
When the Holy Spirit comes in at the moment of salvation, a person is made holy by His presence within and is set apart to live in service for God. This is the work of God in you. This new purpose for your life requires and draws you to give over the entirety of yourself to the Master as you choose less and less of self, and more and more of Him. Ultimately, ideally, you would reach a point of totally giving up yourself and any "rights" to live only for the Master. This is your response to God.