The Times has reviewed receipts from Cash App, a mobile payments app, and Apple Pay that show payments from Mr. Gaetz and Mr. Greenberg to one of the women, and a payment from Mr. Greenberg to a second woman. The women told their friends that the payments were for sex with the two men, according to two people familiar with the conversations.

In encounters during 2019 and 2020, Mr. Gaetz and Mr. Greenberg instructed the women to meet at certain times and places, often at hotels around Florida, and would tell them the amount of money they were willing to pay, according to the messages and interviews.

One person said that the men also paid in cash, sometimes withdrawn from a hotel ATM.

Some of the men and women took ecstasy, an illegal mood-altering drug, before having sex, including Mr. Gaetz, two people familiar with the encounters said.