This really overlaps because racism in action, so to speak, simply means denying someone their basic rights because they have a different skin color. In particular though you seem to allude to the distinction between universal human rights and civil rights. In the United States, African Americans were "technically" equal to whites after the Civil War. The Jim Crow Laws passed in the postbellum period and that the Civil Rights movement in the 1960's fought to end established separate social spheres ( hence the "separate but equal" idea). Schools, for instance, were segregated but even though they were supposed to be equal in standards of quality, that was almost never the case. This is an example of a civil rights violation that Du Bois discusses in his essay Of the Meaning of Progress when he recounts his years of teaching in rural Tennessee. Racism in America problematizes color and strives to deny a person of color or a different race their civil rights.
When we talk about human rights nowadays on the other hand, we most often refer to the Post WW II declaration of universal human rights that was adopted by the United Nations in 1948 in wake of the atrocities of the second World War. Some of these rights are congruent with the codified Civil Laws in the US, such as the abolition of slavery for instance. Further, they have the same origin; they can be traced back to the idea of natural law, the enlightenment tradition and the Bill of Rights in the United States, and the Declaration of the Rights of Man and Citizens in France among others. The major difference between international human rights and the constitutional civil rights of Americans that Du Bois finds violated Souls is that human rights are supranational, they transcend national boundaries.
To recap, the idea of human rights was existent and codified in America within Civil law when Du Bois wrote around the turn of the century, but he worked specifically against racism and for a full realization of Civil Rights for African Americans rather than from within the framework of universal human rights.