CAR 2(7) refers to CAR 206 so if it modifies 206 it gets a bit circular. However, the requirement for an AOC is in the Act not the Regulations, and doesn't refer to commercial operations at all - only "such purposes as are prescribed". CAR 206 prescribes the purposes.
Also refer to CASA Ruling 3/2004, it is possible for an operation to fall into e.g. both airwork and charter.
"An operation classified for more than 1 of the purposes in CAR 206 must comply with the requirements applicable to both classifications"
If it is both airwork and chharter it also falls under more than one definition in CAR 2(7) so these definitions are not exclusive.
CAR 2(7) is a definition, so you need to refer to the sections of the regulations that use the words "aerial work operations", "charter operations", "regular public transport operations" and "private operations" to see where it applies.
If a regulation says "the holder of a PPL must not fly an aircraft in aerial work operations, charter operations or regular public transport operations" I look at those 3 definitions to understand what a PPL cannot do.
If a regulation says "the holder of a PPL may fly an aircraft if it is engaged in a private operation" I look at the definition for a private operation. The aerial work, charter and regular public transport definitions are not relevant to that regulation.