OK: one last try.
A PPL/IR Pilot WITHOUT a commercial licence (CPL) flies a friend from Nantes to Cardiff in a SEP. He is not paid anything. Although the flight carries a level of risk associated with flying in a SEP over water, this flight is perfectly legal.
A few days later, the same pilot, in the same aircraft, flies a different passenger on the same route in identical weather conditions but this time he is operating a grey charter and charges his passenger £500 for the flight. This flight is illegal because the pilot is not allowed to charge for it.
Although it is clearly illegal: why is the second flight inherently more dangerous than the first?
It is not more dangerous, the rules are just more relaxed for a private flight, presumably because each person has made a personal choice to go on the flight, have seen passengers refuse to take a private single engine flight. On a private flight all the passengers will have a personal relationship with the pilot, on a charter the passenger, likely as not, wouldn't know the pilot from the proverbial bar of soap. The regulations require a higher standard of care for fare paying passengers. In my day single engine aircraft were not permitted to be used for a charter requiring over water flight, IMC, or night flying. All because of the associated risk, but a private pilot and passengers have the ability to accept those very same risks. UK regulations are the same are they not? US rules I know not, in any event, does the UK allow US registered aircraft to engage in charter operations within its borders, I doubt it.