Jim Crow Laws enforced segregation between black and white people. The court case "Plessy Vs Ferguson" was trying to please people by enforcing the "separate but equal" law. Basically, they wanted to make the two races separate, but they thought it would be fine as long as both places were the same in quality and quantity.
To sum it up, Jim Crow Laws were to separate the two, but black people were given schools that weren't as good, trashy bathrooms, etc. It was also made to make sure that black people could not go some places on certain days, or at all. The "Plessy vs Ferguson" case was to try to make it better by separating the races, but having both bathrooms the same and both schools the same so none is better than the other.
From the time Savannah held the title of state capital, a majority of Georgia was unhappy with the choice. So by 1847 some were unhappy with Milledgeville and called for an election to move the capital to Atlanta.
