Donald J. Trump once thundered that the questions surrounding Hillary Clinton’s use of a private email server were “bigger than Watergate.” On his 2016 presidential campaign, “where are her emails?” became a Republican rallying cry that was soon replaced with an even more threatening demand: “Lock her up.”

Now, it’s Mr. Trump who faces accusations of improperly taking government records to his private residence. But among Republicans, once so forceful about the issue of mishandling documents, there was little sign of outrage.

Several Republicans who once railed against Mrs. Clinton’s document retention practices did not respond Thursday to questions about Mr. Trump’s actions. Others who had been directly involved with investigating Mrs. Clinton declined to discuss the specifics except to suggest, without evidence, that the National Archives and Records Administration was treating Mr. Trump more harshly.

“Why is the Archives handling this differently?” Senator Charles E. Grassley of Iowa asked in a statement relayed through his spokeswoman.

Although the details differ, the broad strokes of the controversy over a former official’s handling of government documents were strikingly familiar, prompting a wave of Democratic anger — and some painful memories. The fact that Mrs. Clinton was eventually cleared of any wrongdoing only added to the sense of frustration among Democrats.

“There is just the hypocrisy and irony of all it,” said Karen Finney, a Democratic strategist and former Clinton aide, who added that she wasn’t particularly surprised by the new accusations against Mr. Trump. “This is who Donald Trump is. He frequently will attack people falsely for things he is actually doing.”

News reports this week revealed that after a lengthy back and forth between Mr. Trump’s lawyers and the National Archives, the former president handed over more than a dozen boxes of records, including documents, mementos, gifts and letters that he was legally required to leave in the custody of the federal government. Archives officials believe the boxes included classified information. Staff in the White House residence also thought that the president had flushed pieces of paper, after periodically discovering wads of printed paper clogging the toilet, according to a forthcoming book, “Confidence Man,” written by a New York Times reporter, about Mr. Trump and his presidency.

The years long State Department probe of emails sent to Mrs. Clinton’s private computer server concluded with a whimper in 2019, when a State Department investigators sent a report to Congress finding that “there was no persuasive evidence of systemic, deliberate mishandling of classified information.”

Mr. Grassley, who started investigating Mrs. Clinton’s email server in 2017, pushed for a finding nearly three years after the conclusion of the campaign, sparking speculation that Republicans were seeking to revive an issue that had been political advantageous.

In his statement about the charges against Mr. Trump, Mr. Grassley said, “The law is the law, and it ought to be enforced regardless of which party is involved.” He added that he believed the National Archives, at the time “was less inclined” to involve the Justice Department in the recovery of Mrs. Clinton’s emails.

“But now, after the Archives was able to recover presidential records, it seems to want to loop in the Justice Department” he said.

Jason Chaffetz, a former Republican congressman of Utah who as chairman of the House Oversight Committee led extensive investigations into Mrs. Clinton’s emails, said in an interview on Thursday that the two situations were different. Mrs. Clinton, he said, set up a “convenient arrangement” where she stored State Department communications on a private server, in violation of agency policy.

In the case of the former president, Mr. Chaffetz said, he needed to know more about what, specifically, Mr. Trump took from the White House, and if there were duplicate or digital copies of what Mr. Trump had reportedly flushed down the toilet or ripped up. When asked about detailed news reports, Mr. Chaffetz said that this behavior did “not necessarily” constitute destroying records.

“I believe in the sanctity of the federal records,” Mr. Chaffetz said, “but you’re going to have to come up with specific instances.”

In a text message, Liz Harrington, a spokeswoman for Mr. Trump, said that Mr. Trump had worked with the National Archives “to preserve documents that he could have kept in his possession as personal items if he had wanted.”

Several former Trump White House officials, who regularly attacked Mrs. Clinton, had nothing to say about Mr. Trump’s decision to take documents with him to Mar-a-Lago.

But Stephanie Grisham, a former campaign aide who served as White House press secretary for Mr. Trump, said in a text message that the seriousness of consequences for Mr. Trump would hinge on what he took, and also on the broad power he had as president to declassify materials.

“I think the recent revelations deserve scrutiny,” said Ms. Grisham, who has written a book about her time in the White House. “But until it’s known what kinds of information was taken/handled improperly, it’s hard to compare the two.”

Mr. Trump showed little such restraint. His belief that Mrs. Clinton had intentionally mishandled email from her home office became a central focus of his campaign and a rallying cry for his supporters. The idea so fixated him that he called on a foreign government to conduct cyberespionage against a former Secretary of State.

“Russia, if you’re listening, I hope you’re able to find the 30,000 emails that are missing,” Mr. Trump said, referring to emails Mrs. Clinton had deleted from the private account she had used when she was secretary of state. (The Russians, it turns out, might have been listening.)

But questions about the conduct of Trump White House officials quickly emerged. Ivanka Trump, the president’s daughter, and Jared Kushner, the president’s son-in-law and senior adviser, repeatedly used private messaging services for official White House business in a way that may have violated federal records laws. The president’s habit of ripping up documents when he was done with them prompted some aides to retrieve shreds from the garbage and send them to records management to tape them back together.

There were signs Thursday that Democrats may approach Mr. Trump’s possible violations with some of the same fervor as their Republican opponents.

On Thursday, Representative Carolyn B. Maloney, Democrat of New York, said she had asked the National Archives for more information about how the agency had communicated with Mr. Trump about the records he had taken. Ms. Maloney, the chairwoman of House Committee on Oversight and Reform, has promised to investigate whether or not Mr. Trump attempted to destroy records.

For her part, Mrs. Clinton took a lighter approach. On Monday, she shared on Twitter a headline from a Washington Post article detailing Mr. Trump’s habit of shredding documents, along with a link to a cup featuring a famous photo of Clinton, wearing sunglasses and scrolling on her Blackberry.

The slogan embossed on the coffee mug? “But her emails.”