There was little reason to predict those differences when the two men served as law clerks to Justice Anthony M. Kennedy starting in the summer of 1993. “We were in the middle of everything,” Justice Kavanaugh said in a 2017 interview, when he was still an appeals court judge.

The two clerks had already known each other for more than a decade, having attended Georgetown Preparatory School in North Bethesda, Md., together. Justice Kavanaugh, now 54, was in the class of 1983. Justice Gorsuch, 51, was two years behind him.

As justices, though, the two men can be a study in contrasts. “Gorsuch is clearly more willing to sweep with a broader brush, appears less concerned about precedent and does not seem to have the same pragmatic streak that we see a little bit in Kavanaugh,” Professor Adler said.

Justice Gorsuch is a formalist who is committed to the interpretive tools of originalism, which looks to the meaning of the Constitution when it was adopted, and textualism, which focuses on statutory wording. He is suspicious of arguments grounded in pragmatism and impatient with lawyers who will not address him on his terms.

“We hear a lot about what makes sense in this room,” Justice Gorsuch said at an argument last month over whether a criminal statute was unconstitutionally vague. “I’m curious about what the law is.”

When he failed to get a satisfactory answer, he dismissed the lawyer. “Off you go,” he said.

That same day, in a statute of limitations case, Justice Kavanaugh indicated that he was inclined to take account of what makes sense. “If the law is murky and we can choose one path or another reasonably as a matter of law, wouldn’t we choose the more orderly, practical approach?” he asked.

Ross Guberman, an authority on legal writing and the author of “Point Taken: How to Write Like the World’s Best Judges,” said that Justice Gorsuch possesses the showier writing style.