Slaves differ from servants in three important aspects: value, consent, and treatment.
In terms of the value that they are rewarded for their labor, servants are paid for their work, while slaves are not. They are forced to labor for free, and the most that the fortunate among them can expect in return is basic human kindness.
Servants consent to work for their employers but slaves do not. Their labor is both forced and enforced by threats of physical harm and worse. We see this in Chains when Isabel and her sister, Ruth, are originally promised freedom upon the death of their owner, Miss Mary Finch. This promise proves to be worth nothing when a relative of Miss Finch's sells the girls to the Locktons.
Servants are generally treated better than slaves. In Chains, the treatment that Becky, the Locktons' housekeeper, receives from her employers, is practically lavish compared to the treatment that Isabel receives from those very people.