"Slave" is one of the characteristics of Jesus Christ, who in everything, always and everywhere was obedient to God, His spiritual Father and Lord, Creator and Ruler of all Being.

"Slave" of God is a symbol, image, characteristic of a person who, having realized the greatness of God, the Wisdom and Grace of His Laws and Commandments, his subordination to Him, loved his Creator, Lord, Master "with all his heart, with all his soul, with all his strength, with all his mind" and began to serve Him selflessly, selflessly, in everything, obediently doing His Will.

"Servant" of Christ is a disciple, a follower of the Teachings of Jesus Christ, subdued by the spiritual greatness of his Master, fully devoted to the fulfillment and preaching of the Teachings of Jesus Christ. 

Negative Meaning. 

"Slave" of sin is a symbol of a person who is in the slavery of serving only his own flesh, in the slavery of serving various pernicious ideologies, false teachings, false religious beliefs, their founders and spokesmen.