“The more serious issue may be not so much that there has been a violation of the Presidential Records Act, but the reason for a decision to circumvent it,” said Robert F. Bauer, who served as White House counsel for former President Barack Obama. “That is the red flag.”

A White House official insisted that Mr. Kushner and Ms. Trump had never improperly handled classified material.

In the past, Ms. Trump and Mr. Kushner have claimed that they were not familiar with the rules that applied to them. Yet current and former White House officials familiar with the guidance that all aides there are given have said the two were given ample warning. That includes warnings about using chat apps, which are supposed to be prohibited for government business.

The couple has continued to balk at the notion that there are similarities in their circumstances with Mrs. Clinton’s. There are some differences, but there are also a lot of equivalencies, according to lawyer familiar with federal record keeping.

Mrs. Clinton’s case occurred under the Federal Records Act and regulations promulgated by the State Department. Mr. Kushner and Ms. Trump’s case, in contrast, concerns the Presidential Records Act, which was passed in 1978 after the Watergate scandal and declares that all presidential records are public property. The most important thing it did, according to attorneys, was prohibit the destruction of records that are described as private.

Mr. Lowell said at the time that he did not know if Mr. Kushner had communicated classified information on the messaging service, WhatsApp, telling lawmakers that was “above my pay grade.” He argued that Mr. Kushner took screenshots of the communications and sent them to his official White House account or the National Security Council and had therefore not violated federal records laws.

But Mrs. Clinton’s former aides said they were not willing to give Mr. Kushner, in particular, the benefit of the doubt.