1. Different cultures. Despite being living in the same country and having a general "American" culture, there are white and black subcultures, where white and blacks will use different slang and terminology. In fact, there are informal methods that discourage American blacks from talking like American whites. When I was growing up, if you did not speak like other blacks, blacks would say you were "acting white" and you would be criticized and made an outcast. There is a complex history behind this and I don't have enough space to explain it. However, blacks who grew up around whites generally have the same accent as other whites. And I have met whites who lived in black neighborhoods that talk with a black accent. Also, since a lot of blacks are represented in pop culture, there is a lot of black slang that whites have adopted so there is some overlap.

2. Different regions. People from different parts of the country have different accents. Whites and blacks from the south have different accents from white and blacks in the northeast. Whites and blacks in the northeast have different accents from whites and blacks on the west coast. And so on.

Andrew, it's different! Every Brazilian can easily note that there's a huge difference in the accents in terms of race in the US. A group of Brazilian students including me got a scholarship to study in the US in 2013 and our first questions were: Why two peoplet that are born in the same city can have extremely different ways of speaking and huge difference in the accent. 

We have differences in accents but due to region, city and location but not because of race! In my city, if you talk to a black or white brazilian, it's the same accent, you can't ever say that one is white and the other is black, but while I lived in the US, I could tell that I was talking to a black while on the phone. 

The US had segregation for a long time, so even people who lived in the same city developed different accents. Segregation technically no longer exists; but a lot of the old black suburbs are still mostly black and a lot of the old white communities are still mostly white. Of course, this doesn't apply to anyone. A lot of black people don't sound 'stereotypically black'. It's also common for some white celebrities (like Justin Bieber) to mimic African American Vernacular to try to give off a public image.

I believe it's similar to how class accents developed in England: the different classes mixed with each other so infrequently that people in the same city had different accents, depending on what class they were in. Those are mostly disappearing now though.

Different regions have different accents, just like Brazil

Cultural and languages diferenciation is very common in Countries as USA and Brazil that received a lot inmigrants independently of their Skin Colors. Thats not a question of being white or Black, Yellow or green, but, all new influentions that groups of people will develop among them and how people will see the diferences received and adaptations too, as tone of talking on same word, diferent words but same meaning and Slangs.