This is a question for those who take it upon themselves to find who who their fathers are, i.e, doing genealogy research.
For those captured and sold into slavery, and then their descendents who lived through slavery in Europe and the Americas, how exactly have scholars classified them. Are those initially captured considered considered captives, while their progeny is considered slaves? Or are they to be considered slaves and so when looking at lineage certain confusions can be laid to rest by simply using generational consensus on the rules of slaves?
By confusions, an example is where a European "slave master" has a child with his "slave". If the mother was to be considered a captive, then in such a case the child would be considered a child of zina and hence the lineage goes through the mother. On the other hand, if the mother is to be considered slave, then would that not mean that the lineage goes through the slave master?
As for "generational consensus", or simply things that past generations have done without disagrement on the requirement that Islam affirms those actions and hence the generational consensus does not against the shariah, an example would be the famous:
إن المولود يتبع أباه في الإسم والنسب، ويتبع أمه في الحرية والرق، ويتبع خير والديه في الدين
A new born follows his father in name and lineage, and follows his mother in freedom or slavery, and the child follows the parents who had the best religion (for when a child befre puberty dies, and if they are to be prayed over and buried in muslim cemetaries).
Of whom who mentioned this were Ibn Al Qayyim Al Jawziyyah in his أحكام المولود.
Back to the topic at hand, for what Islam has affirmed of Slavery when it came in the time of Ignorance of the Arab, is that what we use for classifying and applying rules to historical individuals important to our personal lineage? Or is the fact that, regardless of how the Arab got their slaves before Muhammad ﷺ sent, Islam officially cut off all forms of slave procuration except for one which was allowable for our ummah, and so the Europeans taking Africans or Natives as captives and their generations of slavery are not to be counted as "Slaves" but as captives?
That was a long question, but I hope it was understandable. Again, to summarise my question, are the generations of slaves in Europe and the Americas to be considered slaves or captives? What have the scholars said on this matter and which scholarly works should be read to further research this matter?