I doubt if the word “slave” appears in any criminal law except as a crime to be punished.
Nowhere does any law define convicts as “slaves” of the state.
So the term applied to convicts is simply a colorful metaphor.
Indeed, we are all arguably “slaves” to some passion or other.
As Jesus said (paraphrase): If you commit a sin you are a slave to sin.
Finally, I think the courts have ruled that states cannot, in effect, treat their prisoners like slaves, not certain just where they draw the lines.
Article XIII (Amendment 13 - Slavery and Involuntary Servitude)
Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction. affects 11