In all, six justices issued opinions, collectively spanning more than 200 pages notable for sometimes harsh language and starkly differing accounts of the nation’s history and the role race plays in contemporary society.

The two sides, for instance, offered competing understandings of the meaning of Brown v. Board of Education, the towering 1954 decision that barred racial segregation in public schools. The lesson of Brown, Chief Justice Roberts wrote, was that “the time for making distinctions based on race had passed.”

Justice Sotomayor said the decision stood for a different principle and accused the majority of engaging in revisionist history. “Brown was,” she wrote, “a race-conscious decision that emphasized the importance of education in our society.”

She added: “At the risk of stating the blindingly obvious, and as Brown recognized, the 14th Amendment was intended to undo the effects of a world where laws systematically subordinated Black people and created a racial caste system. Brown and its progeny recognized the need to take affirmative, race-conscious steps to eliminate that system.”

Justices Thomas and Jackson, the court’s Black members, traded particularly sharp barbs.

“As she sees things,” Justice Thomas wrote of Justice Jackson, “we are all inexorably trapped in a fundamentally racist society, with the original sin of slavery and the historical subjugation of Black Americans still determining our lives today.”

Justice Jackson responded that her colleague’s “prolonged attack responds to a dissent I did not write in order to assail an admissions program that is not the one U.N.C. has crafted,” adding that “Justice Thomas’s opinion also demonstrates an obsession with race consciousness that far outstrips my or U.N.C.’s holistic understanding that race can be a factor that affects applicants’ unique life experiences.”