Ferguson involved a man named Homer Plessy. He was considered colored, though he had 1/8 "black blood" and 7/8 "white blood." He tried to sit on the "white" train in Louisiana, and got kicked out and arrested for it. According to Louisiana state law, it was illegal. He disagreed with the judge's decision that he should spend time in jail or pay a fine and he appealed his case all the way to the Supreme Court. There the justices ruled against Plessy and established the principle "separate but equal", which said that even though facilities were separate, it didn't mean that they weren't equal. .
This decision legalized segregation. Before Plessy segregation was legal only within certain states and certain boundaries, for instance they couldn't segregate interstate trains. After Plessy almost every facility could legally be segregated. Both before and after, many injustices still went on, like sharecropping, lynching, and the KKK terrorized many people. .
Brown involved Linda Brown, a black third grader in Topeka, Kansas, who wanted better schooling than her "black school" provided. A nearby "white school" would have provided that opportunity, but she wasn't allowed there. Her father, Oliver Brown, joined the National Association for the Advancement of Colored People (NAACP) in a crusade to end segregation in schools. They took their case against the Board of Education to the Supreme Court. There the justices overturned the previous standard of "separate but equal." Their decision required state governments to end segregation in schools. After allowing 58 years of segregation, the court was now saying that segregation was not "separate but equal," it was separate and unequal. Schools began to desegregate, but it took a few years to take effect. In theory Brown ended segregation, but because blacks and whites lived in different communities, they still went to separate schools.