WASHINGTON — On the surface, a judge’s ruling on Tuesday night that Congress can obtain Trump White House files related to the Jan. 6 riot seemed to echo another high-profile ruling in November 2019. In the earlier matter, a judge said a former White House counsel must testify about then-President Donald J. Trump’s efforts to obstruct the Russia investigation.

In both cases, Democratic-controlled House oversight committees issued subpoenas, Mr. Trump sought to stonewall those efforts by invoking constitutional secrecy powers, and Obama-appointed Federal District Court judges — to liberal cheers — ruled against him. Each ruling even made the same catchy declaration: “presidents are not kings.”

But there was a big difference: The White House counsel case two years ago had chewed up three and a half months by the time Judge Ketanji Brown Jackson issued a 120-page opinion to end its first stage. Just 23 days elapsed between Mr. Trump’s filing of the Jan. 6 papers lawsuit and Judge Tanya Chutkan’s ruling against him.

The case, which raises novel issues about the scope of executive privilege when asserted by a former president, is not over: Mr. Trump is asking an appeals court to overturn Judge Chutkan’s ruling and, in the interim, to block the National Archives from giving Congress the first set of files on Friday. The litigation appears destined to reach the Supreme Court, which Mr. Trump reshaped with three appointments.

But if the rapid pace set by Judge Chutkan continues, it would mark a significant change from how lawsuits over congressional subpoenas went during the Trump era.

The slow pace of such litigation worked to the clear advantage of Mr. Trump, who vowed to defy “all” congressional oversight subpoenas after Democrats took the House in the 2018 midterm. He frequently lost in court, but only after delays that ran out the clock on any chance that such efforts would uncover information before the 2020 election.

So alongside the substantive issues about executive privilege, one key question now is whether Mr. Trump can again tie the matter up in the courts long enough that even a Supreme Court ruling against him would come too late for the special committee in the House that is seeking the Trump White House documents for its investigation into the Jan. 6 riot.

Specifically, the Jan. 6 committee has demanded detailed records about Mr. Trump’s every movement and meeting on the day of the assault, when Mr. Trump led a “Stop the Steal” rally and his supporters then sacked the Capitol in an attempt to block Congress from certifying Mr. Biden’s Electoral College victory.

The chairman of the committee, Representative Bennie Thompson, Democrat of Mississippi, has said he wants to wrap up by “early spring.” In that case, the committee would need access to the files it has subpoenaed by late winter for that information to be part of any report.

Legally, the committee could continue working through the rest of 2022. If Republicans retake the House in the midterm election, the inquiry would very likely end.

What happens next in the Jan. 6 White House files case may turn on the inclinations of whichever three judges from the U.S. Court of Appeals for the District of Columbia Circuit are randomly assigned to the panel that will hear Mr. Trump’s appeal.

Of the court’s eleven full-time judges, seven are Democratic appointees — including Judge Jackson, whom Mr. Biden elevated earlier this year — and four are Republican appointees, including three named by Mr. Trump. The circuit also has five “senior status” judges who are semiretired but sometimes get assigned to panels; four of those five are Republican appointees.

If the D.C. Circuit rejects Mr. Trump’s request for an emergency stay blocking the National Archives from turning over the files before the case is fully litigated, Mr. Trump would presumably immediately appeal to the Supreme Court via its so-called shadow docket, by which the justices can swiftly decide emergency matters without full briefs and arguments.

If a stay is granted at either level, the question would shift to whether the D.C. Circuit panel echoes Judge Chutkan’s decision to move quickly in light of the circumstances, or throttles back to the slower pace it tended to follow on such cases when Mr. Trump was president.

Notably, in another Trump-era case, involving access to financial papers held by his accounting firm, Mazars USA, the Federal District Court judge assigned to that matter, Amit Mehta, was sensitive to the timing implications and took less than a month after the case was filed in April 2019 to hand down his opinion that Congress could get the records.

But a D.C. Circuit panel took about five more months before reaching that same result — a nominal win for Congress — in October 2019. Mr. Trump then appealed to the Supreme Court, which waited until July 2020 to send the case back down to Judge Mehta to start the litigation over again using different standards.

Separately, House Democrats have introduced legislation in response to the Trump presidency that would, among many other things, speed up lawsuits to enforce congressional subpoenas for executive branch information. Two people familiar with the matter said House Democratic leaders have indicated they plan to hold a floor vote on that bill before the end of 2021, though no date has been set; its prospects in the Senate are unclear.

A related important difference in secrecy disputes between the Trump era and the Jan. 6 White House papers case is that when Mr. Trump was president, his administration controlled the executive branch files Congress wanted to see.

Today, President Biden has refused to join Mr. Trump in invoking executive privilege, instead instructing the National Archives to give Congress the files unless a court orders otherwise. As a result, when it comes to government files, the default has flipped from secrecy to disclosure.

During the phase of the lawsuit before Judge Chutkan, she signaled that she was averse to judicial delay. During arguments last week, she rejected a suggestion by a lawyer for Mr. Trump that she examine each document before deciding whether executive privilege applied.

“I don’t see any language in the statute or any case that convinces me that where a previous president disagrees with the incumbent’s assertion of privilege, that the court is required to get involved and do a document-by-document review,” she said, adding:

“Wouldn’t that always mean that the process of turning over these records, where the incumbent has no objection, would slow to a snail’s pace? And wouldn’t that be an intrusion by this branch into the executive and legislative branch functions?”

Justin Clark, the lawyer for Mr. Trump, responded that he did not think it would be an “unbearable burden” for the judiciary to review each disputed document to make sure that the Constitution was being followed.

The Biden administration’s control of the archival records left by the Trump administration does not, of course, extend to the information inside the heads of the former Trump aides and loyalists whom the Jan. 6 committee wants to testify. Mr. Trump has instructed them not to cooperate with the committee’s subpoenas.

Among those who defied the committee’s subpoenas is Stephen K. Bannon, a Trump ally who worked in the White House until August 2017. The House on Oct. 21 declared him in contempt of Congress and asked the Justice Department to prosecute him.

Any such charges are unlikely to result in swift testimony by Mr. Bannon. In addition to the questions over executive privilege, his case raises a novel twist since he was not an executive branch official at the time of the conversations with the president that lawmakers want to ask about.

Three weeks have passed since that referral and the Justice Department has made no decision about whether to proceed with such a legal process. At a news conference on Monday, Attorney General Merrick B. Garland declined to provide any update.

“This is a criminal matter,” he said. “It’s an ongoing examination of the referral and, as you know, the Justice Department doesn’t comment on those. We evaluate these in the normal way we do — facts and the law, and applying the principles of prosecution.”

Before Mr. Biden appointed him attorney general in March, Mr. Garland had served as a judge on the D.C. Circuit for 24 years.