A lawyer was accused of stealing $1.2 million from his law firm and covering it up. An insurance broker was accused of taking $350,000 from a client and covering it up. And a former president was accused of orchestrating a $130,000 hush-money payment to a porn star and covering it up.

All three men were prosecuted by the Manhattan district attorney, Alvin L. Bragg, and each faced the same felony charge: falsifying business records.

The charge, a staple of his office’s white-collar work, can only be elevated from a misdemeanor to a felony if the defendant falsified the records in an attempt to commit or conceal a second crime.

Although the district attorney’s office is not required to identify the second crime at the outset of the case, Mr. Bragg prosecuted both the lawyer and the insurance broker for additional crimes — including grand larceny — telegraphing why their false records charges were bumped up to felonies. Only the former president, Donald J. Trump, was indicted for falsifying business records, and no other crimes.

A New York Times analysis of about 30 false business records cases brought by Mr. Bragg and his predecessor — based on court records, interviews and information the office provided — shows that in this respect, the case against Mr. Trump stands apart. In all but two of the indictments reviewed by The Times, the defendant was charged with an additional crime on top of the false records charge.

The decision to charge Mr. Trump with 34 counts of falsifying business records — and no other crimes — highlights the unique nature of the case, the first indictment of a former American president. Mr. Bragg, a Democrat, has drawn criticism from Mr. Trump’s allies, who say that he bumped up the charges to a felony for political reasons.

But Mr. Bragg has argued that if the Trump indictment is unusual, it is only because the facts of this case are unusual as well, and the charge must fit the facts: Mr. Trump is accused of covering up a payoff to a porn star to bury a sex scandal in the days before a presidential election.

Mr. Bragg also said, at a news conference on the day of Mr. Trump’s arraignment, that an option for the second crime could be a federal election law violation, under the theory that the hush money illegally aided Mr. Trump’s candidacy.

And on Thursday, Mr. Trump’s lawyers sought to move the case from New York State Supreme Court to federal court, citing those comments as part of the justification for the legal change of scenery. The former president’s lawyers may in part be using the request to move the case as a way to gain more clarity on the second crime.

Mr. Bragg’s supporters, including former prosecutors with the district attorney’s office, have defended his decision not to explicitly mention the second crime in the indictment. They noted that even in the many cases where other crimes are charged, the district attorney’s office never specifies upfront which crime is being used to elevate the false records charge to a felony. In that sense, the Trump case is typical.

“The indictment doesn’t specify it because the law does not so require,” Mr. Bragg said, in his usual lawyerly fashion, at his news conference.

The somewhat unusual nature of the Trump indictment in some ways encapsulated both Mr. Bragg’s skills and shortcomings as district attorney. A career prosecutor, Mr. Bragg has a keen eye for legal strategy but something of a blind spot for the way his decisions are perceived by the public.

His maneuvering on the second crime could provide his prosecutors a strategic advantage in the courtroom, as he keeps Mr. Trump’s lawyers guessing about what it will be. If Mr. Trump’s lawyers convince the judge in the case, Juan M. Merchan, that an election law violation is not viable, Mr. Bragg can pivot to another, like a quarterback calling an audible.

“You’re not in the defendant’s head, so you have to be careful locking yourself into any one thing,” said Karen Friedman Agnifilo, one of the leaders of the office under Mr. Bragg’s predecessor. “And if you don’t have to, why do that?”

For now, though, that means it is unclear how exactly prosecutors plan to argue that Mr. Trump is guilty of 34 felonies, rather than 34 misdemeanors.

“My view is that while the law allows the prosecutor to play it close to the vest, it seems that best practice and fairness requires they reveal — to the extent they know — what the crimes are,” said Marc F. Scholl, who served in the district attorney’s office for nearly four decades in both trial and senior investigative roles. “And because it’s a matter of such public interest,” he added of the Trump case, “you really want to show the world you’re not hiding anything.”

To Mr. Bragg, a former federal public corruption prosecutor, the Trump case is the simple story of a criminal cover-up.

The case centers on the $130,000 hush-money payment to the porn star, Stormy Daniels, who was threatening to go public with her story of a sexual encounter with Mr. Trump. Mr. Trump’s fixer at the time, Michael D. Cohen, paid Ms. Daniels to buy her silence in the final days of the 2016 campaign. Mr. Cohen, who has since turned against Mr. Trump and become Mr. Bragg’s star witness, has said he was acting on Mr. Trump’s orders.

Mr. Bragg’s prosecutors say that Mr. Trump subsequently covered up his reimbursements to Mr. Cohen. The president’s company recorded the repayment to Mr. Cohen as “legal expenses” and cited a retainer agreement — even though there were no such legal expenses, and no such retainer agreement.

Mr. Cohen pleaded guilty in 2018 to federal campaign finance violations one of which stemmed from the hush-money payment to Ms. Daniels. That federal crime is one of the options Mr. Bragg’s prosecutors are mulling for the bump-up crime in the case against the former president.

But nearly every other defendant indicted by Mr. Bragg’s office for falsifying business records was charged in state court with another crime.

Aside from Mr. Trump, The Times could identify only two other defendants in the last decade or so to be indicted solely for felony falsifying records. Under Mr. Bragg’s predecessor, Cyrus R. Vance Jr., a woman was charged for a relatively minor offense: providing a fake social security number to a bank.

And last year, under Mr. Bragg, a man was charged with two felony counts of falsifying business records. But unlike Mr. Trump, that man had two co-defendants on the same indictment charged with grand larceny, which was the second crime prosecutors used to elevate his charges to a felony.

The only other cases in which Mr. Vance or Mr. Bragg brought falsifying records charges — and no other crimes — came when the defendants struck a plea deal before an indictment, a stark contrast from Mr. Trump who has already been indicted and is expected to fight the charges tooth and nail.

The rarity of a stand-alone falsifying business records case stems partly from the low-level nature of the charge. Falsifying business records is an E-felony, the lowest level in New York, so the district attorney’s office often tacks it on in addition to other more serious crimes. And financial fraud investigations typically uncover evidence of multiple economic crimes, giving prosecutors a bevy of options.

Under Mr. Bragg, prosecutors have filed more than 120 counts of falsifying business records against a wide variety of individuals and companies, and in all of those cases, prosecutors charged the crime as a felony, according to the district attorney’s office.

Mr. Trump’s lawyers are expected to demand that prosecutors identify the second crime before trial, but Mr. Bragg may never need to fully reveal his plan. He could argue to the judge that felony false records cases are governed by a 43-year-old New York Court of Appeals case involving a burglary charge, which also requires the intent to commit another crime. In that case, the court held that prosecutors need not reveal a second crime.

If Mr. Bragg’s argument persuades Justice Merchan, Mr. Trump will almost certainly appeal, highlighting the obvious distinctions between a false records case and burglary. The resulting litigation could take years to resolve as his appeal is examined in today’s legal environment, which demands greater transparency from prosecutors than was common 43 years ago.

While the Trump indictment does not reference a second crime, Mr. Bragg suggested three possible options during his news conference: Two versions of an election crime — one state, one federal — as well as tax fraud.

The election law crimes might put Mr. Bragg on uncharted ground, raising the possibility that the courts could throw out or limit the case.

Never before has a New York State prosecutor brought an election law case involving a federal campaign, The Times analysis strongly suggests. An untested case against any defendant, let alone a former president of the United States, raises the risk for Mr. Bragg legally — and could expose him to political blowback.

“The notion that a politician making efforts to hide unflattering information from the American voter constitutes a criminal offense sounds a lot to me like criminalizing politics,” said Thomas Kenniff, a defense lawyer in Manhattan and Mr. Bragg’s Republican opponent in the 2021 race for district attorney.

If Mr. Bragg cites federal election law, Mr. Trump’s lawyers will likely argue that a state prosecutor has no authority to invoke a federal crime. And if he uses a state election law, Mr. Trump’s lawyers are expected to argue that federal campaign finance law explicitly says that it overrides — pre-empts, in legal terminology — state election law when it comes to campaign donation limits.

Yet Mr. Bragg may have found an exception. At his news conference, Mr. Bragg cited a state election law that bars any conspiracy to promote “the election of any person to a public office by unlawful means” — not specifically related to donation limits.

And even if a judge were to reject all election-related second crimes, then Mr. Bragg still has tax fraud to fall back on. Under that theory, his prosecutors could argue that the second crime was an intent — by the Trump Organization and possibly Mr. Cohen — to hide the true purpose of the reimbursement on their state tax returns.

Even though there was no effort to cheat on the taxes, any attempt to misrepresent the purpose of the hush money on tax documents could be considered a tax crime, experts said.

“What it really is to my observation is misusing the federal and presumably state tax system to characterize a transaction falsely,” said Scott D. Michel, a partner at Caplin and Drysdale. Discussing the prosecution’s apparent theory, he said, “You cannot have a tax system where people can abuse the filing process and abuse the reporting process to further criminal conduct.”