Two part answer -
1. Private collect - payer deposits the money into the payer's account as per a private agreement in relation to frequency. CSA rules state the amount can't be less than they assess. But private collect allows some flexibility. For example, payee agrees to accept less $ and payer agrees to pay health insurance for the kids.
2. Generally it means the parents are able to make agreements between themselves and don't need a third party to get involved.
CSA Collect - CSA garnish the payers wages and deposit that $ into the payee's account on a monthly basis. Great when no one is working for themselves and or doing cash in hand jobs. That is kinda where the system falls down.
So example - a teacher is a wage slave, no real way to hide income like self employed people do. But even then, if the teacher does after school tutoring for cash and don't declare it, well that is rorting the system.
Hope the answer helps