WASHINGTON — There were two very different Supreme Courts in the term that just ended.

For much of the last nine months, the court seemed to have defied predictions that the newly expanded conservative majority of six Republican appointees would regularly steamroll their three liberal colleagues.

Rather than issuing polarized decisions split along ideological lines, the court was fluid and unpredictable. There was no longer a single swing justice whose vote would often decide close cases, as Justice Anthony M. Kennedy had until he retired in 2018, or as Chief Justice John G. Roberts Jr. did in the term that ended last summer.

Instead, the center of the court came to include four conservative justices who in various combinations occasionally joined the court’s three-member liberal wing to form majorities in divided cases.

But on Thursday, in rulings that gave states new latitude to restrict voting rights and limited disclosure requirements for big donors to charities, the court made clear that the conservative supermajority is still there, perhaps to emerge in a more assertive way in the term that starts in October, when the justices will take up blockbuster cases on abortion and gun rights.

Over the course of what was until its end a relatively placid term, there were six decisions that split 6 to 3 along ideological lines in argued cases with signed majority opinions.

Overall, the three-member liberal bloc was in the majority in 13 of the 28 divided decisions, having attracted at least two votes from the court’s six-member conservative majority. Those votes most frequently came from Chief Justice Roberts and the three newest justices, all appointed by President Donald J. Trump: Neil M. Gorsuch, Brett M. Kavanaugh and Amy Coney Barrett, who joined the court in October.

After steering the court through the term that ended a year ago, Chief Justice Roberts is no longer in the driver’s seat, said Lisa S. Blatt, a lawyer with Williams & Connolly who argues frequently before the court. “The loss of control by the chief justice felt palpable,” she said.

But even as Chief Justice Roberts lost power, some of the values associated with him — incrementalism and deep concern for institutional legitimacy — remained evident in at least some of the court’s work.

“Notwithstanding President Trump’s three appointments, this term suggests that it’s too early to write an obituary for the Roberts court,” said David Cole, the national legal director for the American Civil Liberties Union. “With the notable exception of its Voting Rights Act decision, in many of its most important decisions, the court adopted the sort of minimalism Roberts has long championed, and by deciding cases narrowly, reached agreement across the predicted partisan divides.”

Many of the term’s more important decisions were unanimous or lopsided. When there were dissents or aggrieved concurrences, the disgruntlement often came from the right.

The court’s ruling that the N.C.A.A. cannot bar modest payments to student-athletes was unanimous. So was, at least on the bottom line, its decision in favor of a Catholic social services agency that refused to screen same-sex couples as potential foster parents.

In that second case, though, three conservative members of the court — Justices Gorsuch, Samuel A. Alito Jr. and Clarence Thomas — issued scathing concurring opinions accusing the majority of issuing a ruling so narrow as to be useless.

The same pattern held in some decisions decided by large majorities. The one protecting the free speech rights of a cheerleader who sent vulgar Snapchat messages was 8 to 1, with only Justice Thomas dissenting. The decision rejecting the latest challenge to the Affordable Care Act was 7 to 2, with Justices Alito and Gorsuch dissenting.

There were, of course, some significant cases even before Thursday in which the Republican and Democratic appointees divided 6 to 3 along the usual lines. In one, the court ruled against a California regulation that allowed labor unions to recruit farm workers on private property. In another, the court ruled that juvenile offenders need not be deemed beyond hope of rehabilitation before they are sentenced to die in prison.

Overall, Mr. Cole said, the court was sensitive to individual rights, particularly ones favored by the right.

“The new court is definitely conservative, but that doesn’t mean it is necessarily hostile to civil liberties,” he said. “It protected many liberties that conservatives favor, including religious liberty, property rights, free speech, the privacy of the home and the right of the wealthy to donate to charities anonymously.”

The court was unanimous 46 percent of the time when all nine justices participated, about five percentage points higher than its average since 2010.

“This term bears the mark of the chief justice in several respects — narrow decisions that seem full of compromise but also decisions that confirm his decidedly conservative stripes,” said Allison Orr Larsen, a professor at William & Mary Law School. “Given the highly-charged cases to come next year, I would expect more of the latter and less of the former.”

Justice Kavanaugh was in the majority more than any other member of the court. Indeed, over his Supreme Court career, which began in 2018 after a tumultuous and highly partisan confirmation fight, he has been in the majority 87 percent of the time in divided cases, beating the career records of all justices appointed since 1937.

In the last term, Justice Kavanaugh was in the majority in divided cases 93 percent of the time, followed by the chief justice, at 86 percent, and the two other Trump appointees, Justices Barrett and Gorsuch, at 79 and 75 percent. Those four justices make up the new center of the court, according to data compiled by Lee Epstein and Andrew D. Martin of Washington University in St. Louis and Kevin Quinn of the University of Michigan.

Before the death of Justice Ruth Bader Ginsburg in September and the arrival of Justice Barrett the next month, voting patterns at the court were more predictable, with four-member liberal and conservative wings and Chief Justice Roberts in the middle.

This term, several justices mostly shared a generally cautious approach, Ms. Blatt said.

“Chief Justice Roberts and Justices Kavanaugh and Barrett strike me as institutionalist,” she said, “meaning they recognize that their place in our constitutional structure depends in large part on the public’s acceptance of the court as an independent branch of government free from politics.”

Justice Barrett is still coming into focus, and early voting patterns can be deceiving. Studies have shown that there are “freshman effects” on the Supreme Court that do not always predict long-term trends. Early in their tenures, for instance, justices are less apt to dissent.

Data on argued cases do not take account of the court’s “shadow docket,” which includes rulings on emergency applications decided after only rushed briefings, without oral arguments and often in late-night orders that contain little or no reasoning. During the Trump administration, such rulings spiked, and the court decided many important cases in such cursory fashion.

Some of those decisions demonstrated the impact of the arrival of Justice Barrett more vividly than the regular docket. Before Justice Ginsburg died, the court sustained state restrictions on attendance at religious services prompted by the coronavirus pandemic. The votes were 5 to 4, with Chief Justice Roberts joining what was then a four-member liberal wing to form majorities in cases from California and Nevada.

After Justice Barrett joined the court, it started to strike down similar restrictions, again by a 5-to-4 vote, with the chief justice now in dissent. Those rulings did more than decide isolated disputes. They articulated a new understanding of the scope of the Constitution’s protection of the free exercise of religion, one that critics said should have been the product of more sustained and careful deliberation.

Something similar happened in a series of emergency applications in election disputes, where shifting majorities of justices tended to rule that federal courts should not change voting procedures enacted by state legislatures even as they declined to interfere when state courts or agencies change those procedures.

But the court in December soundly rejected a lawsuit by Texas asking it to throw out the election results in four battleground states that Mr. Trump had lost. Two months later, the court rejected Mr. Trump’s last-ditch effort to shield his financial records from prosecutors in New York, with no noted dissents.

Justice Stephen G. Breyer, 82, “played a starring role this term,” Ms. Blatt said. Indeed, Justice Breyer — the target of pressure from some activists on the left to retire at the end of the term to ensure that his successor would be considered by the Senate while Democrats control the chamber — wrote consequential majority opinions in several cases, including the ones on the Affordable Care Act and students’ First Amendment rights.

On the whole, Justice Breyer’s voting record in the last term tilted left. He voted with Justice Sonia Sotomayor, the court’s most liberal member, 91 percent of the time in divided cases in which all of the justices participated, up 18 percentage points from the previous term. Only one other pair of justices agreed that often: Chief Justice Roberts and Justice Kavanaugh, also at 91 percent.

At the other end of the spectrum, Justices Alito and Sotomayor agreed just 22 percent of the time. And there were signs of division on the right side of the court. Justices Gorsuch and Kavanaugh, Mr. Trump’s first two appointees, agreed 65 percent of the time, down 20 percentage points from the previous term.

The court decided just 54 argued cases with signed opinions, the second-smallest number since the 1860s. The smallest was in the last term, at 53.

The court’s docket in the term that starts in October may not be larger, but it will contain at least two potentially far-reaching cases: a challenge to the constitutional right to abortion established in Roe v. Wade and the most important Second Amendment case in more than a decade.

Marin K. Levy, a law professor at Duke, said the decision issued on Thursday upholding voting restrictions in Arizona “fundamentally changed how this term will be remembered.”

“It puts an exclamation point on what had otherwise been a fairly quiet term,” she said. “It also sets the tone for next year, when the court will hear cases on hot-button topics including gun regulation and abortion.”