Plessy versus Ferguson was a Supreme Court case addressing a one eighth black person who sat in the whites only section of a Louisiana train, and refused to move. The basis of their argument was that so long as facilities were equal, they could be seperated. The Supreme Court decided that a statute which implies merely a legal distinction between the white and colored races has no tendency to destroy the legal equality of the two races. This resulted in a doctrine known as separate but equal, which was applied to a vast number of other facilities and allowed for the constitutionality of segregation.
Brown versus Board of Education was actually the name given to a series of five cases heard by the Supreme Courts, so the facts between cases differed. However, the main issue was the constitutionality of state sponsored segregation in public schools. The basis of their argument was that segregated school systems had a tendency to make black children feel inferior to white children. The Supreme Court decided that in the field of public education, the doctrine of separate but equal has no place. Separate educational facilities are inherently unequal. This resulted in the slow desegregation of public schools, and encouraged the desegregation of other facilities.