You are right, but the details are a bit of.

So there were two kinda of slavery. For Israeli the concept of indentured slavery was applied: 7 years and then you were free. But if you married during that time and had children, your wife and children remeined slaves.

So masters tried to find wife's for their indentured slaves, because most likley people won't leave back their family after 7 years. So Israeli slaves could pledge themselves to their masters for live.

When you buy a male Hebrew slave, he shall serve six years, but in the seventh he shall go out a free person, without debt. 3 If he comes in single, he shall go out single; if he comes in married, then his wife shall go out with him. 4 If his master gives him a wife and she bears him sons or daughters, the wife and her children shall be her master’s, and he shall go out alone. 5 But if the slave declares, ‘I love my master, my wife, and my children; I will not go out a free person,’ 6 then his master shall bring him before God. He shall be brought to the door or the doorpost, and his master shall pierce his ear with an awl, and he shall serve him for life.

Exodus 21:2-11

For non Israeli (Gentils) their was just plain and simple slavery.

44 As for the male and female slaves whom you may have, it is from the nations around you that you may acquire male and female slaves. 45 You may also acquire them from among the aliens residing with you and from their families who are with you who have been born in your land; they may be your property. 46 You may keep them as a possession for your children after you, for them to inherit as property. These you may treat as slaves, but as for your fellow Israelites, no one shall rule over the other with harshness.

Leviticus 25:44-46