How did the Northern view of equality differ from the Southern view?

The North and South had different societal views on equality, usually based on race or color of skin. However, these differences start long before the Civil War, with the North becoming more industrial and the South becoming more agricultural. This simple difference flows into two distinct societal types.
The North, at least in some places becomes more urban, where people of many races all work in the factories. Meanwhile, in the South, as agriculture explodes, they are in need of more workers. The majority of their workforce is brought in from other countries, mostly Africa, and used as slave labor. For many reasons, Southerners enforced slavery to the maximum amount possible. Slaves are humiliated, beaten, worked to death, starved, and separated from their families, and all of these things are purposefully completed so that the slaves may understand their "worth" and "standing" in southern society. The lack of equality by race in the south becomes a way of keeping slaves from rising up and changing that society.
As time goes on, the apparent differences between northern and southern societies clash again and again as more states are added to the union each year. Northern society is beginning to free any slaves it may have. Meanwhile, southern society has made slavery and racial in equality the backbone of its society, industry, and way of life. All of this leads to southern states seceding from the union, as northern activists become adamant in their campaigning of the "evils" of the south's slavery. The northerners have lived side by side with peoples of many races for years at this point, and thus come to believe that all people have those rights set forth by their forefathers. However, generations of southerners have come to believe that whites are superior and blacks are inferior simply based on equality. Therefore, equality is deemed only accessible to some.

In the North before the Civil War, equality was equated to freedom. Everybody had the same right to be free, meaning no person could be owned outright by another person or bought or sold by another. Nobody could be enslaved.
In the South prior to the Civil War equality equated to freedom only for whites. People who were black could be enslaved. Some black people could buy their freedom if their masters allowed it, and others were set free by their masters, but this was solely at the discretion of the owner. A Southern black person had no inherent right to freedom from slavery. To be a black was often defined in the South as having as little as "one drop" of black blood. This meant the child of a white slave owner and a black slave was designated black, as were the grandchildren and great-grandchildren, even if in all these cases, one of the parents was white.
In any case, the Civil War decided the question of freedom according to Northern ideals in which all people were, by right, born free. The South, however, maintained more legal separation between blacks and whites than was common in the North, opting for the idea of "separate but equal." Blacks were sent to separate schools, for example, but in reality these schools were not afforded equal resources to white schools.