The regulation that slices and dices the classifications is actually CAR 1988 2(7):
Actually, no. The requirement for an AOC is defined in the Act.
CIVIL AVIATION ACT 1988 - SECT 27
AOCs
(2) Except as authorised by an AOC,
(or various permissions for foreign aircraft):
(b) an aircraft shall not operate in Australian territory
...
(9) Subsection (2) applies only to the flying or operation of an aircraft for such purposes as are prescribed.
Then CAR 206:
CIVIL AVIATION REGULATIONS 1988 - REG 206
Commercial purposes (Act, s 27(9))
(1)
For the purposes of subsection 27(9) of the Act (my bold), the following commercial purposes are prescribed:
So CAR 206 very explicitly is the regulation that defines when an AOC is required.
So an activity that is listed in CAR 206
and CAR 2(7)(d) would require an AOC, but be allowed under the privileges of a PPL, e.g.
agricultural operations on land owned and occupied by the owner of the aircraft;
Is an agricultural operation (CAR 206 (1)(a)(iii)) and a private operation (CAR 2 (7)(d)(iii)).
A red tractor is still a tractor.