Don't worry: All of this will be made clear in the new 1998 regulations. When they come in, there will be no need for CAOs.
Until then....
I think your interpretation is correct.
The key provision that gives you your definition of e.g. "charter aircraft" is regulation 2(6) of the CARs 1988:
(6) For the purposes of these Regulations, an aircraft shall be classified in accordance with the type of operations in which it is being employed at any time, as follows:
(a) when an aircraft is being employed in aerial work operations, it shall be classified as an aerial work aircraft;
(b) when an aircraft is being employed in charter operations, it shall be classified as a charter aircraft;
(c) when an aircraft is being employed in regular public transport operations, it shall be classified as a regular public transport aircraft;
(d) when an aircraft is being employed in private operations, it shall be classified as a private aircraft.
I can't be bothered looking up the reg linking the defined terms in the regs to the Orders.