What is the difference between a servant and a slave, and how does this relate to Chains by Laurie Halse Anderson?

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.

Peter Wood, a professor of history at Duke University, was asked this very same question.  His answer has always surprised me because I always assumed that the difference between a servant and a slave was that a servant could legally choose to quit, while a slave could not do that.  Wood's description of the difference between slaves and servants is quite interesting.  
A servant could be a white person or black person.  Skin color doesn't make a difference.  The defining feature of a servant is that he or she is under contract to work for a certain number of years.  When the contract time runs out, that person is free to leave and seek out another contract if desired.  What I find interesting about Wood's response is that he says owners occasionally treated their servants worse than their slaves because the owner knew that he/she had the servant for a limited time.  In essence, the servant was the equivalent of a rental, while the slave was actual property and needed to be taken care of.  
In Isabel's situation though, Isabel was treated much more poorly as a slave than Becky was treated as a servant.