She did not address questions about the details of the $35,000 severance arrangement with the other woman. A spokesman for Mr. Cain, J. D. Gordon, also declined to discuss the details of the arrangement.

Asked about the encounter that, according to friends and former colleagues, had made the woman uncomfortable at the restaurant association, Mr. Gordon said, “Mr. Cain has already explained the situation in some detail in numerous public appearances.”

Four people with contemporaneous knowledge of the encounter said it had taken place in the context of a work outing during which there had been heavy drinking — a hallmark, they said, of outings with an organization that represents the hospitality industry. They spoke on condition of anonymity to avoid being publicly drawn into the dispute, and declined to provide details of the encounter, saying they did not want to violate the privacy of the woman.

Two of them said that other factors had been involved in her severance, and that other workplace issues had been making her unhappy at the association as well. But they said the encounter with Mr. Cain had added an emotional charge and contributed to the size of her payment. One former colleague familiar with the details said such a severance was not common, especially for an employee with the woman’s relatively short tenure and her pay grade.

The situation with the other woman appeared to be more in keeping with a standard settlement related to harassment allegations, though she never filed a lawsuit in a case that, one person familiar with her accusations said, included “more than one” claim of an incident that made her feel uncomfortable.

Mr. Cain has at times seemed to conflate the situations with the two women. Appearing to speak about the terms of the formal settlement with Mr. Bennett’s client on Monday, he said she had received perhaps three months of severance — this after at first saying he knew of no severance.

On Tuesday, he said in an interview with HLN that it was “in the vicinity of three to six months.”

Asked Tuesday on the Fox News Channel why his account kept changing after the report appeared Sunday on Politico.com, Mr. Cain said, “When I first heard the word ‘settlement,’ I thought ‘legal settlement.’ ”He added, “My recollection later is that there was an agreement.”