The “Black Belt” is the area where blacks live in high numbers in the American South.
You are indeed correct about Africans staying put after emancipation. There are other dynamics too, like WW2 when many moved to the San Francisco Bay Area to do menial labor.
But for the most part, black people live where their ancestors lived.
Another thing I find interesting is agriculture and black people overlap, and conversely places that historically had very little agriculture to this day possess very few black people. Arizona, New Mexico, Alaska, et al.
People move for a reason. I think the term for this field of study is “Cultural Geography”.
It’s actually called the black belt in Alabama because of the soil, but it is indeed where many black people also live. I think Southerners as a whole tend to be homebodies and stay put. We have deep ties with the land. Even during the worst days of Reconstruction, folks hung on or moved to another part of the South. It’s hard to explain, but being a Southerner is similar to being a Texan.