What is the difference between a private and a commercial flight according to the US Customs and Border Protection? From what I understand, whether or not a flight is classified as private or commercial in the eyes of US Customs and Border Protection (CBP) has nothing to do with the Federal Aviation Regulations (FAR) flight rules that they are operating under. For instance, I understand that I can legally be operating under FAR Part 91 and still be a commercial flight in the eyes of CBP. What then is the determining factor?
According to the CBP eAPIS FAQ, this definition is in 19 CFR 122.1:


  (d) Commercial aircraft. A “commercial aircraft” is any aircraft
  transporting passengers and/or cargo for some payment or other
  consideration, including money or services rendered.
  
  [...]
  
  (h) Private aircraft. A “private aircraft” is any aircraft engaged in
  a personal or business flight to or from the U.S. which is not:
  
  (1) Carrying passengers and/or cargo for commercial purposes;
  
  (2) Leaving the U.S. carrying neither passengers nor cargo in order to
  lade passengers and/or cargo in a foreign area for commercial
  purposes; or
  
  (3) Returning to the U.S. carrying neither passengers nor cargo in
  ballast after leaving with passengers and/or cargo for commercial
  purposes;