Did Jim Crow laws that enforced segregation have a long term goal like Apartheid South Africa which wanted to make different countries for each group?
It can be argued that the end game of Jim Crow laws was to create two separate societies, with the end goal of removing the 'unwanted' from society.
This goes beyond just racism and into eugenics. According to this site, the outcome of Plessy V Ferguson ' represented the legitimization of two societies: one white, and advantaged; the other, black, disadvantaged and despised.' Interracial marriage became outlawed, and different levels of society were molded
The Eugenics movement in the US, according to wikipedia started in the 1880s and continued into the 1920s. Couple tidbits from the page:
The Immigration Restriction League was the first American entity associated officially with eugenics. Founded in 1894 by three recent Harvard University graduates, the League sought to bar what it considered inferior races from entering America and diluting what it saw as the superior American racial stock (upper class Northerners of Anglo-Saxon heritage).
With the passage of the Immigration Act of 1924... inspired by the eugenic belief in the racial superiority of "old stock" white Americans as members of the "Nordic race" (a form of white supremacy), strengthened the position of existing laws prohibiting race-mixing.
I would argue that the idea was to make a holy, one true race to better society. Something like genocide was the extreme of this, but US society was content to restrict immigration and procreation of the 'unwanted'
Can someone expound on the South Africa part of this question?
In the 19th century following Reconstruction, the end game for segregation was to recreate the conditions of slavery as much as possible. Jim Crow laws compromised Black civil, social and economic rights. The Grandfather Clause prevented Black voting. Share cropping mimicked the economic relationship of slavery. And lynching brought back terrorism as the enforcement mechanism to keep Blacks in their place.
After achieving its end game which was "slavery by another name" the segregationists fought afterwards a defensive battle to continue their system. "Segregation today, segregation tomorrow and segregation forever," was the slogan coined by George Wallace.
Segregation was an emotional response more than a rational response. The 20th century segregation leaders were not deep thinkers who contemplated an end game.