In readings about early modern Ottoman life, references to white and black eunuchs often pop up. I assumed at first that white eunuchs were those of European or West Asian stock, while black eunuchs would have been Sudanese or Sub-Saharan African. In hindsight, though, I realize that I'm applying modern American racial ideas onto a much earlier culture.
What was the difference between a white eunuch and a black eunuch? Was this an actual Ottoman term, or something created by Christian observers? Did skin color play a role at all?
A good bit of your question has been answered before if you'd like some back-reading! Safe to say yes those eunuchs did fill different roles based on their race, and I might even be able to spin a decent argument that they were somewhat different genders.
Now that you've made me think about it, truth be told I don't know for sure if black/white was a direct translation of the Ottoman terms for them. However, I think it was, because Western European travelogues (which were directed at home readers) would sometimes take the time to assure their readers that the white slaves were "not really white."