I'm not an expert on slavery in the US but I do know something about it in the Roman world. The biggest difference was it was not linked to ethnicity. You could become a slave through war, being captured by pirates, and early in Rome's history - through debt. This meant that any ethnicity could be a slave (though trends tended to follow wars): Greek, Germanic, African, Persian, etc... While some early Greek philosophers thought that the easteners were more 'slavish' by nature than the freedom loving Greeks, I'm not sure how much of that belief/trope carried through to the Romans.

Another important difference was that Rome manumitted a large amount of slaves and incorporated them into their civic body. Unlike Greek states where citizenship was jealously guarded, Rome granted a freed slave Roman citizenship and placed them under the patronage of their former master - already integrating them into the traditional Roman client/patron relationship. While there was certainly elite stigma over freedmen, I'm not aware of any examples of more plebeian discrimination towards them.

Edit: at home and was able to answer some questions from a source: Invisible Romans by Robert Knapp which tries to look at all those ignored in elite narratives.

I know a bit about American slavery. As Agrippa911 said the biggest difference was slavery's connection to race. This took on a deeper role in America slavery. It was believed that if black slaves were freed then they would roam the South being lazing, having sex with white women, seek vengeance against their former owners and generally be unproductive. Slavery and religion became intertwined in the South and the system was considered a part of the Southern way of life. Because slavery was so tied up with race many non-slave holders in the South protected the institution. Slaves in the South were rented out to non-slave owners for cheap labour as well. The entire financial system of the South was based on slavery. Mortgages were procured with slaves held as collateral, cotton was sold in markets where they would be transported to the North to factories, and the largest capital in America was held in slaves. In other words the total value of slaves in America exceeded that of all the capital in all the banks and insurance companies.

A big change in American slavery came in 1807 with the closing of the Trans-Atlantic slave trade. It became illegal to import slaves from Africa (though this still happened regularly.) Because slaves could not be imported several slave owners began breeding slaves for sale. This is led to the internal slave market of America. As the South expanded westward the demand for slaves increased dramatically. In response many slave traders simply kidnapped freemen from the North and sold them into slavery (Solomon Northup).

Edit spelling. And sorry about not providing sources I have to get back to a paper on Chiam Rumkowski. If you pm me I can get you some sources. If you’re interested in American slavery I suggest reading Frederic Douglas’ My Bondage, My Freedom. It’s an amazing book written by a former slave about his life in slavery. He is also very smart and articulate so his information is very useful.

I don't have much to add about American slavery unless you feel like you need more to get research started. I got nothing on Roman slavery. If you want to read one book on American slavery I suggest Ira Berlin's Many Thousands Gone: The First Two Centuries of Slavery in North America. It is brilliant and gives a comprehensive overview of slavery in North America in one book.