Cohen was talked into pleading guilty to a non-existent crime. It is not a crime to pay off a person on behalf of a client, and get reimbursed later, and it’s not anything to do with campaign laws.
The case that the U.S. Attorney for the Southern District of New York has made is that the payment of hush money to stop two women from going public with potentially damaging information during campaign season is an illegal campaign contribution. By pleading guilty, Cohen has agreed with that assessment.