The question, then, is whether prosecutors have more convincing factual evidence to present to a jury about Mr. Trump than they did in the case of Mr. Edwards. Legal experts pointed to several major differences.

For one thing, one of the payments to Mr. Edwards’s mistress took place as he was ending his candidacy, which further muddied how to interpret his motivation. By contrast, the payments to Ms. McDougal and Ms. Daniels came just ahead of the election.

For another, prosecutors in the Edwards case had little corroboration from other key figures in the transactions to explain their motivation. One of the supporters of Mr. Edwards who provided the funds, Fred Baron, had died, and the other, Bunny Mellon, was a 101-year-old recluse prosecutors did not seek to drag into the courtroom as a witness.

By contrast, a key figure in both of the Trump transactions, Mr. Cohen, is available as a witness and has already admitted his principal purpose in helping pay off the women was to “suppress the stories and thereby prevent them from influencing the election,” as the sentencing memo said.