No, slavery generally is considered forcing someone to work for free and the person is generally enslaved as a matter of prejudice: sometimes because their considered inferior by race, sometimes because they’ve been captured in war, sometimes because they are considered inferior for some other reason like belonging to a different tribe. Some slaves are born into slavery, but the prejudice that enslaved their parents tends to be why they themselves are considered slaves as well.

The key here is it’s forced upon them and they aren’t usually paid for it.

Prison labor doesn’t fit that description. For one thing they’re almost always paid, granted at a reduced rate but this is typically because a portion of their earnings are used to offset their costs (prisons aren’t free to operate.) A prisoner might be forced to work but many prison labor programs are voluntary, at least the better jobs require some amount of cooperation by the prisoner.

Finally, a prisoner has been imprisoned because they violated a law, a jury of their peers found them guilty of that crime and the judge believed a fair and equal punishment was to incarcerate the individual. Though not always perfect in the USA criminal court is designed to favor allowing a guilty person to go free if the evidence is lacking verse punishing a potentially innocent person-the so called 99% certainty rule. This is much different than how slaves were generally come by.