A slave is a person who is physically owned or property of another who has either inherited or bought that person. He has no rights of his own and must obey and preform the work which his owner demands.
A saint is a person who has received the blessing of salvation through Christ Jesus who paid the full price of his salvation with His precious life's blood. This salvation places one in an exceptional position, an exalted position, a holy position.
Both the slave and the saint owe their obedience to their master, the one who purchased them. The slave if unwilling to be a slave, will be miserable, as force is used to make him comply to his master's demands. The saint on the other hand realizes that he has been bought and saved from a horrible pit and been lifted to an amazing position. The saint has a different mind-set because of the grace of God, his Master, which has been revealed to him by God's Spirit.
Mankind, who has been bought with such a costly ransom, can choose to be miserable denying the grace of God or choose to be thankful rejoicing in the Gift and Mercy of God.
The Christian's relationship with the Lord can be viewed as both a slave, one bought and owned, and as a saint, one who has been lifted up to a position in Christ. Also the Christian's relationship is affected by his attitude to both of these ideas of who he really is in Christ Jesus. He humbles himself as a slave and is obedient, even as Christ was, yet as he is obedient he rejoices as a saint because of the his New Life in Christ Jesus. As a slave the Christian is obedient and as a saint he is obedient.