Were the Children of a Slave of an Israelite also Slaves?

I’ve often heard said Ancient Israel practiced a form of slavery different than the chattel slavery practiced by antebellum America. I’ve read what the Torah has to say about slavery, but can’t find anything explicit about whether the child of a (non-Israelite) slave would be considered a slave, as they would have been in the States. What was the practice historically? And what does the Talmud say on the subject? (Not asking about the Israelite slaves of other Israelites).

PS: I’m not a biblical slavery apologist. My question is motivated by an interest in the history and the history of interpretation. Not a desire for moral guidance.