The main idea of a slave is one that have being bought by another, and once purchased you now the property of the buyer. so the slave is committed to his / her master and committee to service, the service is one of compulsory, in which the slave has no choice in what aspect of the job he or she will do but is expected to do the will of the master
The root idea of a saint is one who is dedicated to to another. so in essence both a slave and a saint differ but are the same, because a slave is dedicated to his or her master just as much as the saint.
Our relationship with God should stem from the same idea that we are bought by the blood of Jesus and we are consecrated or dedicated - set a part for God's Purpose. our whole live should be about serving our Lord and walking in obedience to His will and carry out the task he has called us to do.
which is serve and be the saint in Christ. we have being consecrated to do God's will and a servant with only one master.
The two words have the same meaning to me as a servant of God, we should all have a serving heart and humble so God can use us for His will and complete our destiny