Slavery in the Ottoman Empire (and islam in general) was very different from the chattel slavery of the Americas. While the vast majority of American slaves were agricultural workers, most slaves in the Ottoman Empire were employed in military or domestic roles. Most important for your question, there wasn't a racial component to Ottoman slavery. While slaves brought to the Americas were enslaved exclusively from black africans, black africans were simply one of many sources of slaves for the Ottomans. Furthermore, black Ottoman slaves were enslaved for religious reasons, rather than ethnic ones. Islam has restrictions on Jewish, Muslim, and Christian slaves, but has no such restrictions for pagans, and thus black pagans from the Sudan and East Africa were a profitable target of slavery.

In general, Ottoman (and muslim) slavery was much less generational than American chattel slavery. If a slave converted to islam, there was a high chance of he/she being freed, or at least their children being freed, in their lifetimes. Finally, black slaves in particular were prized as eunuchs, with the head of the imperial harem being the Chief Black Eunuch (and other notable families employing black eunuchs as status symbols while mimicking the Imperial court), which tended to limit crossbreeding.